I call this a shrinking gap question.

Currently, Train A is 15 miles ahead of Train B.
So, the GAP = 15 miles

Train A is traveling at 40 miles per hour and Train B is traveling on a parallel track in the same direction at 60 miles per hour.
Speed difference = 60 mph - 40 mph = 20 miles per hour
So, the GAP shrinks at a rate of 20 miles per hour

How many minutes will it take Train B to catch up with Train A?
In others how long will it take the GAP to decrease from 15 miles to 0 miles.

Time = distance/rate
= (15 miles)/(20 miles per hour)
= 3/4 HOURS
= 45 minutes

Answer:
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One approach

relative speed=60-40 =20 (same direction)

time = 15/20 *60 =45 min

other approach


0 hr 30 min 45min

A mile 15 35 45 (train A moves 40 miles in each hr so it moves 20 miles in 30 min and 10 mile in 15 min)

B mile 0 30 45 (train B moves 60 miles in each hr so it moves 30 miles in 30 min and 15 mile in 15 min)


Answer: A

We are given that train Train A is traveling at 40 miles per hour and Train B is traveling on a parallel track in the same direction at 60 miles per hour. We need to determine how many minutes it will take Train B to catch Train A, since Train B must travel 15 more miles than Train A. Since both trains are traveling for the same amount of time, we can let each time = t hours.

Thus, Train A’s distance is 40t and Train B’s distance is 60t.

Since Train B travels 15 more miles than Train A:

40t + 15 = 60t

15 = 20t

15/20 = 3/4 = t

3/4 hour = 45 minutes

Answer: A
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D=S*T
The question asks how long will it take to cover 15 miles with a relative speed of 20 mph (same direction so subtract speeds)

15=20*T, hence T=\(\frac{15}{20}\) hours =\(\frac{15}{20}\)*60 mins = 45 mins
Answer A

\(\frac{15}{(60-40)}*60\) = 45 Minutes...

Answer must be (A) 45
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Without formulas and using some approximation

In 1 hr train A would have travelled 15+40=55 miles
In 1 hr train B would have travelled 60 miles. This means train B passes train A before hitting 60 minutes.
The only answer less than 60 is A

Train A is traveling at 40 miles per hour and Train B is traveling on a parallel track in the same direction at 60 miles per hour. Currently, Train A is 15 miles ahead of Train B. How many minutes will it take Train B to catch up with Train A?

Speed (Train A) = \(40 \frac{Miles}{Hour}\)

Speed (Train B) = \(60 \frac{Miles}{Hour}\)

Distance Between Train A and Train B = 15 Miles

As both Train A and Train B are moving in the same direction, we have to subtract the higher speed from the lower speed to get the relative speed

= \(60 \frac{Miles}{Hour}\) - \(40 \frac{Miles}{Hour}\) = \(20 \frac{Miles}{Hour}\)

So, lets calculate the time required for Train B to catch-up with Train A:

\(Time = \frac{Distance}{Speed}\)

\(= \frac{15}{20}\)

= 0.75 Hrs

As the time asked in the question is in minutes we will multiply it by 60

\(= 0.75 * 60\)

\(= 45 Min\)


Hence, the Answer is A
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Distance = 15 miles
Difference between the speeds = 60 - 40 = 20 mph
Time taken = 15/20 = 3/4 hr = 45 min

Relative speed is 20 miles /hr. i.e the gap is closing at 20 miles /hr.

So if 20 miles gets closed in 60 mins, then 1 mile =60/20, then 15 miles= 60/20*15=45 mins

My approach is like that.

A:40mph A is 15 miles ahead.
B:60mph 60-40 = 20 miles distance

In 1 hr A --> 15 + 40 = 45 miles
In 1 hr B ---> 60 miles. So B is 15 miles ahead. What I want is B to catch up with A, so I want 45 miles both.

in 1 hr --> 60 miles
in x hrs --> 45 miles x= 3/4. we want minutes so 3/4 ( * 60 ) = 45 minutes

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