A train travels from station A to station B. If it travels

Question

A train travels from station A to station B. If it travels at a speed of 100 miles per hour, it ends up reaching the station 30 minutes late. If it travels at 120 miles per hour, it reaches the station 15 minutes early. What is the amount of time that the train is scheduled to take for the journey and what is the distance between the stations?

(A) 2 hours, 225 miles
(B) 3 hours, 350 miles
(C) 4 hours, 450 miles
(D) 5 hours, 550 miles
(E) 6 hours, 650 miles

(A) 2 hours, 225 miles
(B) 3 hours, 350 miles
(C) 4 hours, 450 miles
(D) 5 hours, 550 miles
(E) 6 hours, 650 miles

SOURH7WK · Accepted Answer

Let t be the usual time and x be the distance between A & B. So we need to find t and Distance x. The question gives us 2 combinations of speed & time, but the distance remains the same for both condition.

Equation 1 - x= 100 (t+.5) (converted 30 mins into hr) added .5 hrs because it is late or took more time than usual.
Equation 2 - x= 120 (t-.25) subtracted .25 hrs because it is early or took less time than usual.

Now equating 1 & 2 we get 100(t+.5)=120(t-.25)
=> 10t +5 = 12t - 3
=> 2t=8 => t= 4 hrs.
Hence x= 100(4+.5) =>100 X 4.5 => 450 miles.

Hence correct answer C.

monirjewel · Answer

Let D be the distance between the two stations A and B.
Equation 1, 100(T+.5)=D
Equation 2, 120(T-.25)=D
So, 100(T+.5)=120(T-.25)......Solving two equations, T=4
100(4+.5)=450
C is the correct ans.

EvaJager · Answer

Let  D  be the distance between the two stations A and B. 
We can write directly the equation  \frac{D}{100}=\frac{D}{120}+\frac{3}{4} , because at speed 100mph the train is late by half an hour, at 120mph is early by a quarter of an hour, 
so the difference between the two times is +0.5 - (-0.25) = 0.75.
Solving for  D  we obtain  D=450  (now we already know that the answer is C) and the time is 450/100 - 0.5 = 4 hours.

Answer C

thutran · Answer

T is the the scheduled time. 
s1 = 100, t1 = t+30
s2 = 120, t2 = t-15
since speed varies inversely with time (when distance is kept constant). So if the speed ratio in the 2 cases is s1/s2 = 100/120 = 5/6, time taken in the 2 cases will be in the ratio t1/t2 = 6/5

(t+30)/(t-15) = 6/5
t = 240 mins = 4hrs
d=s*t = 100*4.5 = 450
answer: C

jlgdr · Answer

Good question 100 (t+30) = 120 (t-15) t = 240 minutes = 4 hours C is your correct answer Hope it helps Cheers! J

PareshGmat · Answer

Distance = Speed * Time

t = ideal time

100 (t+30) = 120 (t - 15)

t = 240 = 4Hours

Answer = C

In the OA, had 4 hours been in more than one option, then distance would also required to be calculated

mathiaskeul · Answer

Creating an equation is easy here. We know that both times and speeds can be put in ONE equation. At 100 miles per hour, we're 30 minutes late so we add 1/2. At 120 miles per hour, we substract 1/4 because we're 15 minutes (or a quarter of an hour) early.

100*(t+1/2)=120*(t-1/4)
100t+50=120t-30
Divide everything by ten just to make things easy
20t=80 or 2t=8
This means that the time is four hours. The only answer choice with four hours is C

Testing 450 miles:

100(4+0.5)=450
100(4-0.25)=450

KarishmaB · Answer

Using Ratios:

If Speeds are in the ratio 5:6, time taken will be in the ratio 6:5. The difference of 1 is actually equal to 45 mins ie. 3/4 of an hour. 
So time taken in 1st case is 6*(3/4) = 4.5 hrs = 4 hrs 30 mins.
Since it is 30 mins late, it is scheduled to take 4 hrs for the journey.

Answer (C)

KarishmaB · Answer

Responding to a pm: Check out these posts to understand ratio scale and multiplier concept: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... of-ratios/ https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... os-in-tsd/ We know that the time taken for the two speeds is in the ratio 6:5. This is a difference of 1 on the ratio scale between them (because 6-5 = 1) But we know that in actual value terms, the difference between time taken for them is 30+15 = 45 mins. Say the actual time of arrival is 12 o clock. If it travels at 100 mph, it reaches at 12:30. If it travels at 120 mph, it reaches at 11:45. So the difference between the time taken in the two cases is 45 mins (which is 3/4 of an hour). So the multiplier is 3/4 hr. Time taken in first case = 6*(3/4) Time taken in second case = 5*(3/4)

Rajdeep1989 · Answer

Use the trial method to do fast and easily.

Usually we take the Middle one to start with.

Lets try Option C.

Speed is 100 miles/hr so in 4 hrs it reaches 400 miles ie lags 50 miles which is nothing but distance it can travel in 30 mins! (100m in one hr so 50m in half hr).

We dont need the second hint actually.

bumpbot · Answer

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A train travels from station A to station B. If it travels

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