
By: drstevewu (offline) Monday, July 15 2013 @ 03:23 AM CDT (Read 1234 times)



drstevewu 
Hi, I am trying to solve these 2 speed questions:
1. Mary walked from home to the Church. For the first 2 minutes, she was walking at an average speed of 50 m/min. When she realized that she was going to be late for 5 minutes, she quickly increased her speed by 10m/min. As a result, she was late by 2 minutes. What is the distance between her home and the Church?
2. A delivery man has to deliver a parcel from Town A to Town B by a certain time. If he travels at an average speed of 96km/h, he will arrived at Town B 1/3 hour late. If he travels at an average speed of 90km/h, he will arrived at Town B 1/2 hour late. What is the distance between the two towns?
Thank you for your help..
Cheers,
Steve..

Junior
Registered: 04/20/10 Posts: 31





By: echeewh (offline) Monday, July 15 2013 @ 04:51 PM CDT



echeewh 
Hey there,
In view that both questions are similar, you can use the method shown in Q1 to try and work out Q2 on your own (Ans: 240 km). Should there be any problem, please do let me know.
Following is my worked solution to Q1.
Q1.
***  alignment purpose
H **************************** C

> ** > ********** > ** >
M ** M1 ********* M2 ** M3
s(MM1) = 50 m/min
t(MM1) = 2 min
d(MM1) = 50 × 2 = 100 m
From M1, if M travelled at the original speed of 50 m/min, she would be late by 5 mins. I.e. M would be at M2 and it would take M another 5 mins at that original speed to reach C.
s(M1M2) = 50 m/min
s(M2C) = 50 m/min
t(M2C) = 5 min
d(M2C) = 50 × 5 = 250 m
From M1, if M were to increase her speed to 60 m/min, she would be late by 2 mins. I.e. M would be at M3 and it would take M another 2 mins at that speed to reach C.
s(M1M3) = 60 m/min
s(M3C) = 60 m/min
t(M3C) = 2 min
d(M3C) = 60 × 2 = 120 m
At M1, if M travelled at 50 m/min, M would be 250 m away from C; while M travelled at 60 m/min, M would be 120 m away from C. At this juncture, the time taken for both instances are the same. I.e.
t(M1M2) = t(M1M3)
When time is constant, the distance ratio is the same as the speed ratio. I.e.
s(M1M2) : s(M1M3)
50 : 60
5 : 6
d(M1M2) : d(M1M3)
5 : 6
d(M1M3)  d(M1M2) = d(M2M3) = d(M2C)  d(M3C)
6u  5u = 250  120
1u > 130
d(M1M3) = 6u > 6 × 130 = 780 m
Distance HC = d(MM1) + d(M1M3) + d(M3C)
= 100 + 780 + 120
= 1000 m = 1 km
========
Trust this helps.
Do let me know again if this is different from your <Answerkey> or if there's further clarification
Cheers,
Edward

Active Member
Registered: 04/21/11 Posts: 627





By: drstevewu (offline) Friday, July 26 2013 @ 10:49 AM CDT



drstevewu 
Thank you Edward...

Junior
Registered: 04/20/10 Posts: 31



