Cars A and B are traveling from Town X to Town Y on the same route at

NOTE: When two cars travel in the same direction at different speed x, y (x>y). Then relative speed of faster Car with respect to slower car = x-y. i.e. per hour the distance between faster and slower train will be increased at the rate of (x-y).

Let's see, what happens after 1:30 pm. Car A, whose speed is 1.25 times the speed of car B will increase the distance between the two cars at the rate of (1.25B-B) per hour = .25B.

so at 2:30 pm distance between car A and car B will be (.25B)*1 = .25B
at 3:15 Car A has traveled for additional 45 minutes = 3/4 hr. hence the distance increased by car A in these 45 minutes = .25B(3/4)

so the total distance between A and B, when Car A reaches town Y = .25B+.25B(3/4)
=\(\frac{7B}{16}\)

this distance between A and B is equal to 35 as per the question. hence we have \(\frac{7B}{16}\) = 35
or B= 80
so speed of A = 1.25(80) = 100

let speed of B = x mph
Therefore speed of A = 1.25x mph

By the time A reaches Destination, B is 35 miles behind the destination.
and time taken by A to keep a 35 miles gap with B is time between 1:30 pm and 3:15 pm => 1.75 hrs

therefore => 35/(speed of A - speed of B) = 1.75
35/(0.25x) = 1.75

on solving for x => 80 i.e speed of B

Speed of A = 80*1.25 = 100

hence E

Let speed of B: s. Then speed of A:1.25s

Car A and B are together at 1:30 PM.

Car A reaches Town Y at 3:15 PM.

so A takes (1hour 45 minutes) to reach town Y (This is the time taken after A meets B)
Distance travelled by A: (1hour 45 minutes) * 1.25s

Now in this 1hour 45 minutes, Y is travelling with a speed s. It covers a distance D = (1hour 45 minutes) * s

Equation: D+35 = (1hour 45 minutes) * 1.25s

1hour 45 minutes = 1.75 hours.

1.75s +35 = 1.75 * 1.25s

s works out to 80.

Speed of A = 1.25 *80 = 100 mph.

E is the answer.

This question becomes very simple if you think in terms of distance.
According to stem at 1.30PM they were at same place but at 3.15PM(105mins or 7/4hour) car A was 35 miles ahead.
So difference in their speed = 35/(7/4)= 5*4= 20 miles/hour.
Now we know A's time is 25% less than B's time. due to inverse proportionality we know A' speed was 25% more than B's.
So our eqn becomes Speed of A-Speed of B= 1.25B-B=.25B=20. Speed of B = 80.
But don't fall for trap answer now as stem asks Speed of A which is 25% more.
So answer is 100 miles/hr.

Cars A and B are traveling from Town X to Town Y on the same route at constant speeds. Car A is initially behind Car B, and Car A’s speed is 1.25 times Car B’s speed. Car A passes Car B at 1:30 pm. At 3:15 pm, Car A reaches Town Y, and at that moment, Car B is still 35 miles away from Town Y. What is the speed of Car A?
(A) 60 mph
(B) 75 mph
(C) 80 mph
(D) 96 mph
(E) 100 mph

let d=distance from passing to Town Y
d/(d-35)=5/4
d=175 miles
175 miles/1.75 hrs=100 mph
A's speed is 100 mph

hi! thank you for this answer . Why do we put D+35 while equating? Why not just 35?

Very helpful. Thanks

Let A be the average speed of car A, thus B will be the same for said vehicle.

We know, according to the question, that A = 1.25B

Also, we know that B lost 35 miles in 1h 45 min -> 7/4 hours.

So, in order to know how many miles per hour does B lose to A: 34/(7/4) = 20.

We know now that car A is 20 mph faster, so:

\(A = B + 20\)

\(B+20 = 1.25B\)

B = 80
A = 1.25*80 = 100.

In 1 hour 45 minutes, car A drives 35 miles more than car B.

For relative speed of bodies moving in same direction, the equation is (Sx - Sy) X t = Distance

1 hour 45 minutes = \(\frac{7}{4}\) hour
Relative speed = \(1.25x-x=0.25x=\frac{1}{4} x\)

\(\frac{1}{4} x*\frac{7}{4}=35\)
\(x=80\)

\(∴1.25x=100\)

Let d be the distance from the first meeting point to point Y.

\(Va = 1.25Vb\)
\(d = Va * t\)
\(d - 35 = Vb * t\)
\(d = 175\). Given, the time taken by A from first meeting point to Point Y = \frac{7}{4} Hours
\(175 = Va*\frac{7}{4}\)
\(Va = 100mph\)

From 1:30 pm to 3:15 pm, the time elapsed is 1 hour 45 minutes, or 1.75 hours. We see that during this time, Car A travels 35 miles more than Car B since its speed is 1.25 times that of Car B. Therefore, if we let r = speed of Car B, we can create the equation: .

(1.25r)(1.75) = 1.75r + 35

1.25(1.75r) = 1.75r + 35

1.25(1.75r) - 1.75r = 35

0.25(1.75r) = 35

1.75r = 140

r = 140/1.75 = 140/(7/4) = (4 x 140)/7 = 4 x 20 = 80

Since Car A’s speed is 1.25 times the speed of Car B, Car A’s speed is 1.25 x 80 = 100 mph.

Answer: E

rate a: 1.25b
rate b: b

3:15h - 1:30h = 1:45h = 105/60

during this interval:
a traveled 105/60(1.25b)
b traveled 105/60(b)
their difference is 35
35=105/60(1.25b)-105/60(b)
b=80
1.25b=80, b=100

Ans (E)

Here's an alternative explanation! We can use backsolving, but before doing so lets set up the equations!
This formula is key: Rate*Time = Distance

Car A’s speed is 1.25 times Car B’s speed = Rate(A) = 1.25Rate(B)
Car A passes Car B at 1:30 pm. At 3:15 pm, Car A reaches Town Y = The Total Time that Car A travels is 1 hour and 45 mins (or 7/4 hours)

Rate(A) * \(\frac{7}{4} Hours\) = D
Rate(B) * \(\frac{7}{4} Hours\) = D - 35 miles
So when we choose the answer choices, we can plug those numbers into Rate(A) and Rate(B) to find out which speed would have a 35 mile difference!

Because the time is \(\frac{7}{4} Hours\) and Rate(A) = 1.25Rate(B), it would be smart to pick an answer choice that is divisible by 4, so lets test out C = 80
If Rate(A) = 80 mph, then Rate(B) = 64 mph

80 mph * \(\frac{7}{4} Hours\) = 140 miles
64 mph * \(\frac{7}{4} Hours\) = 112 miles
Difference is only 28, so Rate(A) has to be LARGER than 80, so eliminate A,B,C

Now let's choose answer choice E, as it's also divisible by 4 too
If Rate(A) = 100 mph, then Rate(B) = 80 mph

100 mph * \(\frac{7}{4} Hours\) = 175 miles
80 mph * \(\frac{7}{4} Hours\) = 140 miles
The difference is exactly 35 miles, so E has to be the Answer!

Can ignore the point up until Car A and Car B "meet" (when Car A passes Car B at 1:30 P.M.)

From 1:30 P.M. -- until -- 3:45 P.M.

Car A and Car B are both traveling over the Same Time.

Since the Time Traveled is Same, the Speed at which each Travels is DIRECTLY PROPORTIONAL to the Distance Covered by each.

Speed A = (5/4) * Speed B

Ratio of ----- Speed A : Speed B = 5 : 4

which will EQUAL

Ratio of ---- Distance Covered by A in the 1 hr 45 min : Distance Covered by B in the 1 hr 45 min.

A covered the full distance to Town Y. Say that A traveled a Distance = d

This means that B covered a Distance = d - 35


We can now find the distance from the Point at which they Meet at 1:30 and Town Y.

Ratio of: 5 : 4 = d : d - 35

In Fractional Form: 5/4 = d / (d - 35)

Solving for d: d = 175 miles

A covers this entire distance of 175 miles in 1 hour and 45 minutes (or 7/4 hours)

Thus, Speed A = miles traveled / hours taken = 175 / (7/4) = 100 m.p.h.

Answer E

Haha, this is tricky, it took me good 5 minutes to get to the Speed of car B then I rushed to choose 80, just to figure out seconds later it must be 100, this definitely could happen in the real exam and it would distract me alot to find out I missed 5 minutes and lost an opportunity to solve a hard question that can make or break my score, someone should read the question again before clicking goodbye to it.