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 By: geniuskids (offline)  Tuesday, August 20 2013 @ 05:44 AM CDT (Read 2415 times)
geniuskids

Q1) Kelvin travelled 2/5 of his journey at 45km/h and 1/3 of the remaining journey at 90km/hr. The rest of the journey was completed in 1.2h at an average speed of 100km/h. What was the total time taken for the whole journey?

Q2) A car and a truck were travelling in the same direction along the same road at an average speed of 70km/h and 58 km/h respectively. At 08 00, the truck was 20km ahead of the car. Half an hour later, the truck broke down.

(a) How far was the truck from the car when it broke down? Answer : 14km
(b) At what time did the car pass the truck? Answer : 0842

Pls explain. Thanks

Active Member

Registered: 11/12/11
Posts: 169

 By: echeewh (offline)  Wednesday, August 21 2013 @ 05:25 AM CDT
echeewh

Hi <geniuskids>,

Following are my worked solutions:

Q1.

(2/5)journey at 45 km/h -- (1)
(1/3) of remaining journey = (1/3) × (3/5)journey
= (1/5)journey
(1/5)journey at 90 km/h -- (2)
Rest of journey = (2/5)journey -- (3)

Distance (for rest of journey) = 100 × 1.2 = 120 km
So, (2/5)journey = 120 km

in (2)
(1/5)journey = 60 km
time taken (for (1/5)journey) = 60 ÷ 90 = (2/3) hr = 40 mins

in (1)
time taken (for (2/5)journey) = 120 ÷ 45 = (8/3) hr
= 2 hr 40 mins

1.2 hr = 1 hr 12 min

2 hr 40 mins + 40 mins + 1 hr 12 mins
= 4 hr 32 mins

==========

Q2.

*** - for alignment purpose

|---------------------------------------|
|-> ****** |->
C ******* T
sC=70 * sT=58
tC=0800 tT=0800

(a)

d(CT) = 20 km

sC - sT = 70 - 58 = 12 km/h
Time taken = Extra Distance / Extra Speed
Extra Distance (travelled by C) = 12 × (1/2) = 6 km

Given initial distance apart between C and T is 20 km and C managed to travel an extra distance of 6 km in this (1/2) hr ,

Distance apart between C and T = 20 - 6 = 14 km

(b)
After T broke down at 0830,
Time taken for C (to catch up with T)
= 14 ÷ 70 = (1/5) hr = 12 mins

Hence, time in which C passed T = 08 30 + 00 12 = 0842

==========

Trust this helps.

Do let me know again if there's further clarifications.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

 By: geniuskids (offline)  Wednesday, August 21 2013 @ 05:51 AM CDT
geniuskids

Hi Edward,

Thank you very much for your help. I shall digest the solutions soon.

Active Member

Registered: 11/12/11
Posts: 169

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