Problem Solving

13. Carl drove from his home to the beach at an average speed of 80 kilometers per hour and returned home by the same route at an average speed of 70 kilometers per hour. If the trip home took hour longer than the trip to the beach, how many kilometers did Carl drive each way?
(A) 350
(B) 345
(C) 320
(D) 280
(E) 240


Hi,
The answer is D) but I could not figure out.... can you help?

A difference of speed caused a difference of One? hour For which of the options does this match up? That will be your answer.

Which leads me to think that maybe the Question is worded wrongly.

Neo, thanks so much for your help.

Sorry, I think one word bolded was missing from the text...

13. Carl drove from his home to the beach at an average speed of 80 kilometers per hour and returned home by the same route at an average speed of 70 kilometers per hour. If the trip home took 1/2 hour longer than the trip to the beach, how many kilometers did Carl drive each way?

All right, since we know its 30mins, look for the answer options that are multiples of 70 and 80 and then divide with 70 and 80 and see which one of them will give you a difference of 30mins.

In this case, only 280 since 280/70 = 4hrs and 280/80 = 3.5hours hence 280kms

Just posting an alternative for the equation inclined...

From the question, we know that time taken for (trip-home = trip-beach + 1)

Let x be the distance between home and beach.

x/80 + 1/2 = x/70
(x + 40)*70 = 80x
x = 280

13. Carl drove from his home to the beach at an average speed of 80 kilometers per hour and returned home by the same route at an average speed of 70 kilometers per hour. If the trip home took 1/2 hour longer than the trip to the beach, how many kilometers did Carl drive each way?
(A) 350
(B) 345
(C) 320
(D) 280
(E) 240

Time = D/S
Let distance be x
x/70 - x/80 = 1/2
10x=5600/2
10x = 2800
x=280
Hence D