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 By: Jolynn (offline)  Tuesday, August 21 2012 @ 06:36 AM CDT (Read 2551 times)
Jolynn

Can anybody help me by giving me a solution for the following question so that I can explain to my son. Thanks

Q1)

Martha walks from her home to the stadium at an average speed of 60m/min daily.
On a certain day, she woke up late and left her home 10mins later than usual.
Martha wanted to reach the stadium at her usual time, so she increased her speed by 20m/min.

Q2

A delivery van driver had to deliver goods from the warehouse to the shop.
The van was travelling at an average speed of 50km/h for the first 20minutes.
The driver took a wrong turn and realised that he was going to be late by 10minutes.
So he increased his speed to 75km/h. When he arrived at the shop, he found that he was
early by 6minutes. How far away is the shop from the warehouse?

pls help!!!!

Newbie

Registered: 05/01/10
Posts: 3

 By: GIM (offline)  Wednesday, August 22 2012 @ 09:20 AM CDT
GIM

Q1 solution

Let D be the dist from home to stadium
Usual speed ------> 60 m/min ; Time --------> T mins
Faster speed -----> 80 m/min ; Time --------> (T- 10) mins

Under usual condition,
D1 = 60 x T = 60 T

Based on the 2nd speed,
1 min --------> 80m
10 min ------> 80 x 10 = 800m (started 10 mins later)

Increase speed condition,
D2 = 80 x T - 800m = 80T - 800
Or
D2 = 80 x (T - 10) = 80T - 800

Since the distance travelled for both speed is from home to stadium, therefore D1 = D2
D1 = D2
60T = 80T - 800
20T = 800
T = 40 mins

D = 60m/min x 40min = 2400 m = 2.4 km

Regular Member

Registered: 11/07/10
Posts: 70

 By: GIM (offline)  Thursday, August 23 2012 @ 11:32 AM CDT
GIM

Q2 solution
{-------------------20 mins-----------------}
X___________________________Y________________________Z
Warehouse______________took wrong turn_________________shop

Distance travelled for 1st 20 mins -----> 50km/hr x 20/60hr = 50/3 km

Took a wrong turn at Y, to travelled from Y to Z, he can either:
Travelled at S = 50km/h, T = T + 10/60h; D1 ----> 50 x (T + 10/60)
Travelled at S = 75km/h, T = T - 6/60h ; D2----> 75 x (T - 6/60)

To travel from Y to Z, he can either travel at 50 km/h, but late for 10 mins or travel at 75 km/h and be early by 6 mins.
Since D = S x T and D1 = D2, therefore

50 x (T + 10/60) = 75 x (T - 6/60)
50T + 50/6 = 75T - 45/6
25T = 95/6
T = 19/30 hr

Distance from Y to Z ---> 50km/h x (19/30 + 10/60)hr = 40 km
Total Distance from X to Z---> 40km + 50/3 km = 56.67 km (answer)

Alternative solution:

Difference in time can be written as the following expression:
Since T = D/S and difference in time is [10/60 hr -( -6/60 hr)], therefore

D/50 - D/75 = 10/60 - (-6/60)
(75D - 50D)/3750 = 16/60
25D = 1000
D = 40 km

Total distance travelled ----------------> 50/3 + 40 = 56.67 km (answer)

Sorry for using the wrong speed, I've it corrected!

Regular Member

Registered: 11/07/10
Posts: 70

 By: tancrowhurst (offline)  Saturday, August 25 2012 @ 01:34 AM CDT
tancrowhurst

May I know why is the Distance assumed to be the same please? After taking a wrong turn, isn't driver going to travel a longer distance?

Newbie

Registered: 05/05/12
Posts: 8

 By: tancrowhurst (offline)  Saturday, August 25 2012 @ 01:46 AM CDT
tancrowhurst

Oh, I figured the same distance refer to from the point the wrong turn was made. A mistake was made with the second speed though...it should be 75 km/h not 70 km/h.

Newbie

Registered: 05/05/12
Posts: 8

 By: Ashley Lee (offline)  Saturday, August 25 2012 @ 06:46 AM CDT
Ashley Lee

for Q1:
ans. is 2400m =2.4km

for Q2:
ans. is 63.33km

understand?

Ashley Lee

Newbie

Registered: 08/25/12
Posts: 1
Location: -

 By: angeliakwok (offline)  Saturday, August 25 2012 @ 09:26 AM CDT
angeliakwok

Martha walks from her home to the stadium at an average speed of 60m/min daily.
On a certain day, she woke up late and left her home 10mins later than usual.
Martha wanted to reach the stadium at her usual time, so she increased her speed by 20m/min.

this is an inverse method: As the distance is constant, speed is inversely related to time
Speed is either 80m/min or 60m/min

Ratio of Speed is 4u : 3u
Ratio of time is 3u : 4u

Difference in time unit is 1u equal to 10min, therefore

Using time unit as 3u: actual time is 30mins
Distance is 30 x 80 = 2400m = 2.4km

or

Using time unit as 4u: actual time is 40mins
Distance is 40 x 60 = 2400m = 2.4km

Newbie

Registered: 02/17/11
Posts: 5

 By: angeliakwok (offline)  Saturday, August 25 2012 @ 09:35 AM CDT
angeliakwok

A delivery van driver had to deliver goods from the warehouse to the shop.
The van was travelling at an average speed of 50km/h for the first 20minutes.
The driver took a wrong turn and realised that he was going to be late by 10minutes.
So he increased his speed to 75km/h. When he arrived at the shop, he found that he was
early by 6minutes. How far away is the shop from the warehouse?

Inverse method works too.

Speed is 75km/h or 50km/h

Ratio of speed is 3u : 2u
Ratio of time is 2u : 3u

Time unit difference is 1u = 10 + 6 = 16min. Therefore

Using time unit as 2u: actual time is 32mins
Distance is 32/60 x 75 = 40km

or

Using time unit as 3u: actual time is 48mins
Distance is 48/60 x 50 = 40km

However this is not the end. This is only the distance from the lost point.
Add the initial distance of 20/60 x 50 = 16 2/3 + 40 = 56 2/3km

Newbie

Registered: 02/17/11
Posts: 5

 By: GIM (offline)  Saturday, August 25 2012 @ 12:39 PM CDT
GIM

Yes, I've made the mistake of using the wrong speed in my solution. The speed should be 75 and not 70. With that the answer is 56.67 km. Sorry for the confusion.

Regular Member

Registered: 11/07/10
Posts: 70

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