Sam and Chris leave City A for City B simultaneously at 6 A.

Question

Sam and Chris leave City A for City B simultaneously at 6 A.M in the morning driving in two cars at speeds of 60 mph and 80 mph respectively. As soon as Chris reaches City B, he returns back to City A along the same route and meets Sam on the way back. If the distance between the two cities is 210 miles, how far from City A did Sam and Chris meet?

A. 60 miles
B. 120 miles
C. 30 miles
D. 180 miles
E. 150 miles

Show Answer

Official Answer

D

A. 60 miles
B. 120 miles
C. 30 miles
D. 180 miles
E. 150 miles

MacFauz · Accepted Answer

Time taken by Chris to reach City B = 210/80 = More than 2.5 hours

In 2.5 hours, Sam travels 60*2.5 = 150 miles

So distance at which they meet should be greater than 150 miles.

Only D satisfies.

Answer is D.

KarishmaB · Answer

You can use ratios to solve it easily.

Let's say, they meet x miles away from city A. Sam has covered a distance of x miles and Chris has covered a distance of 210 + (210 - x) = (420 - x) miles.

The speeds of Sam and Chris are in the ratio 60:80 i.e. 3:4. So in the same time, they will cover distance which will be in the ratio 3:4 too.

x/(420 - x) = 3/4
7x = 1260
x = 180 miles

Answer (D)

GyanOne · Answer

Equate the time taken (which will be equal for both). 
=> x/60 =  /80
=> x = 180

Option (D).

PareshGmat · Answer

Look at the diagram, lets say they meet at point P (Which is distance x from start)

Both will take same time to reach point P

Setting up the equation

\frac{x}{60} = \frac{210}{80} + \frac{210-x}{80}

\frac{x}{3} = \frac{420-x}{4}

x = 180

Answer = D

GyanOne · Answer

When Sam and Chris meet, they have collectively travelled 210*2 = 420 miles
=> Distance from city A that they meet = 60 * (420/140) = 180 miles

Option (D).

Fdambro294 · Answer

Because the answers are nice and spread apart, we can use approximation

(1st) where will Sam be when Chris has reached City B? How far will Sam have traveled when Faster Chris travels the 210 miles?

Since the Time spent traveling is the SAME/Constant for both Sam and Chris———> the Speed they travel at will be directly proportional to the Distance they Cover

Sam speed : Chris speed = 60 : 80 = 3x : 4x

When Chris covers 210 miles:

4x = 210

x = 52.5

Sam will have covered a distance of: 3x = 3 * (52.5) = 157.5

This means that once Chris reaches the end and is ready to turn around, Sam has already traveled 157.5 miles.

Therefore, the answer must be greater than 157.5 miles away from the starting point

Only one answer works:

D

Posted from my mobile device

mohammadfaraaz123 · Answer

Thanks for the article VeritasKarishma Your articles on Mixture and allegations problems and TSD ratio have been a great help!

bumpbot · Answer

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Sam and Chris leave City A for City B simultaneously at 6 A.

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