Car A and B started at different times from Town X and travel to Town

Question

Car A and B started at different times from Town X and travel to Town Y on the same route at different constant speeds. Car A was initially behind Car B, but Car A was faster. Car A passed Car B at 1:30 pm. At 3:15 pm, Car A reached Town Y, and at that moment, Car B was still 35 miles away from Town Y. The time Car B took to complete the trip from Town X to Town Y was 25% more than the time that Car A took. What is the speed of Car A?

A. 60 mph
B. 75 mph
C. 80 mph
D. 96 mph
E. 100 mph

A. 60 mph
B. ﻿﻿75 mph
C. ﻿80 mph
D. ﻿﻿96 mph
E. 100 mph

ankushsambare · Answer

Let Car A's speed = A mph and Car B's speed = B mph.
At 1:30 pm, Car A catches and passes Car B.
From 1:30 pm to 3:15 pm = 1.75 hours.
In these 1.75 hours:
 
 Car A reaches Town Y. 
 Car B is still 35 miles away from Town Y.  
So, in the same 1.75 hours, Car A traveled 35 miles more than Car B.
Therefore:
1.75(A − B) = 35
A − B = 20
So,
A = B + 20
Also, Car B took 25% more time than Car A for the whole trip.
Since both traveled the same distance, speeds are inversely proportional to times.
If B's time is 1.25 times A's time, then:
A/B = 1.25
A = 1.25B
Substitute into A = B + 20:
1.25B = B + 20
0.25B = 20
B = 80
Therefore,
A = 100
 Answer: E(100 mph)

KarishmaB · Answer

Use Ratios. Given: The time Car B took to complete the trip from Town X to Town Y was 25% more than the time that Car A took. So to travel same distance of XY, B took 25% more time i.e. their ratio of time taken TimeA : TimeB for equal distance is 4 : 5. So ratios of their speeds SpeedA : SpeedB = 5 : 4 In the time from 1:30 to 3:15 (which is 1.75 hours) i.e. in same amount of time, their distance covered would be in the ratio of their speeds i.e. 5 : 4. This difference of 1 is given to be 35 miles which means that in this time, car A covered 5*35 = 175 miles. Speed of car A = \frac{Distance}{Time} = \frac{175}{1.75} miles/hour = 100 mph Answer (E) Time Speed Distance Using Ratios Concept Video: https://youtu.be/7ASEIvxYPCM

BongBideshini · Answer

Speed of Car A = A
Speed of Car B = B
Now, from 1:30 pm to 3:15 pm, the time is constant. Let the distance from the meeting point to the destination be D
So, Speed  \propto   Distance
 \frac{A}{B} =\frac{D}{D-35}

Next, the time taken by car B to complete the journey is 1.25times the time taken by car A
Here, Distance is constant. 
So, Speed  \propto    \frac{1}{Time}

\frac{A}{B} =\frac{1.25}{1} 
 \frac{A}{B} =\frac{5}{4} 
 \frac{D}{D-35} = \frac{5}{4} 
5D - 175 =4D
D=175 miles
time =(3:15 -1:30) =1:45 =7/4 hr
Speed of A=175*4/7 =100 mph
 Ans E

Car A and B started at different times from Town X and travel to Town

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Car A and B started at different times from Town X and travel to Town

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