1. Motion word problem

I am practicing from a book with the answers but not the details, so I would like the step-by-step information so I can understand and learn. Could you help?

Q: ROUND TRIP SITUATION:
A man drove from his home to a distination and back again (along the same road) in 10 hours. His average speed going was 20 mph and on the return was 30 mph. How long did he take in each direction and what distance did he cover each way?

How do I show an equation here? And How do I solve this? I know (the book gives the answer) that 120 miles is the distance each way and 6 hours going and 4 hours returning. Please explain step-by-step.

Thank you,
tbutlip

2. Re: Motion word problem

Originally Posted by Tbutlip
I am practicing from a book with the answers but not the details, so I would like the step-by-step information so I can understand and learn. Could you help?

Q: ROUND TRIP SITUATION:
A man drove from his home to a distination and back again (along the same road) in 10 hours. His average speed going was 20 mph and on the return was 30 mph. How long did he take in each direction and what distance did he cover each way?

How do I show an equation here? And How do I solve this? I know (the book gives the answer) that 120 miles is the distance each way and 6 hours going and 4 hours returning. Please explain step-by-step.

Thank you,
tbutlip
Let x = the one-way distance in miles

Going one way, his rate was 20 mph.
distance = rate * time
distance/rate = time
x/20 = time to go in one direction

Going the other way, his rate was 30 mph. How long did it take to travel that "x" miles?
x/30 = time to go in the other direction

We are told that the total time is 10 hours

time going one way + time going the other way = 10
(x/20) + (x/30) = 10

Solve that for x...and you will know the one-way distance. You can then find the time going in each direction. And the total distance of the trip, of course, would be 2x.

3. Re: Motion word problem

Thank you sooo much.
tbutlip

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