KarishmaB wrote:
alexpavlos wrote:
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?
A. 20
B. 34
C. 38
D. 40
E. 46
Here is the ratios approach to the problem:
Shannon drives at the speed of 2R in both the cases so she takes the same time. In the first case Maxine reaches home 40 mins after Shannon. In the second case, Maxine reaches 2 hrs after Shannon. Why did Maxine take 1 hr 20 mins extra in the second case? Because she drove at half the speed.
Speed1: Speed 2 = 2:1
Time 1: Time 2 = 1:2 ( since distance stays the same)
The difference between Time1 and Time 2 is 1 hr 20 mins = 80 mins. So Time 1 must be 1hr 20 mins i.e. time taken by Maxine when she drives at speed 2R. Time taken by Shannon must be 1 hr 20 mins - 40 mins = 40 mins (because she reaches 40 mins early)
When their speeds were same in the first case,
Time taken by Maxine : Time taken by Shannon = 80 mins :40 mins = 2:1
Distance traveled by Maxine : Distance traveled by Shannon = 2:1
Total distance is 60 miles so Maxine lives 40 miles away and Shannon lives 20 miles away from office.
I solved this question as following:
Maxine traveled the distance from her work to her house "DM" twice, once by car at a rate 2R mph and the second time by bike at a rate R mph.
Since the distance is the same, time and rate will vary inversely: (t+2/3)/t+2 = R/2R = 1/2 (t is the time Shannon is taking to drive to her house and 2/3 hours=40 min)
From the above, we can solve for t, hence t=2/3 hours
At first, both Shannon and Maxine drove by car to their houses at the rate 2Rmph.
Since the rate in this case is the same, time and distance will vary directly:t/(t+2/3) = DS/DM (DS and DM are Shonnon and Maxine respective distances to their houses from work).
Replacing t by 2/3, we get DS/DM=1/2
Therefore,
DS:DM:TOT
1:2:3
(knowing that the actual total distance is 60, the unkown multiplier would hence be 20)
DS:DM:TOT
20:40:60
So DM= 40 and correct answer is DDear
KarishmaBI figured that this question can be solved algebraically as well as suggested by Bunuel above but I have been unsuccessful trying to solve this question using relative speed. Can this question be solved using relative speed to start with? If not can you please explain why?
Thank you so much!
This is not a relative speed question because they are not covering the 60 miles "together."
They are each covering their own distance in their own time. Shannon arrived early and stopped while Maxine kept going.
Had they covered a certain distance together in the same time, relative speed would have come into play.