A boy travels a distance of 60km cycling at a speed of 20km per hour. If the boy stops for a 20 minute rest each half hour throughout the journey and he reaches his destination at 4pm.What time did the boy start his journey?

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- Jan 5th 2012, 05:17 AMMathBondTime algebraic question.
A boy travels a distance of 60km cycling at a speed of 20km per hour. If the boy stops for a 20 minute rest each half hour throughout the journey and he reaches his destination at 4pm.What time did the boy start his journey?

- Jan 5th 2012, 06:02 AMHallsofIvyRe: Time algebraic question.
Well, what have

**you**done on this? How long would it take to go 60 km at 20 km/hr? How many "half hours" are there in that? So what total length of time did he spend resting? - Jan 5th 2012, 07:23 AMBobtheBobRe: Time algebraic question.
It isn't all that difficult if you think about it. HallsofIvy says it all but just as a little hint, you know that $\displaystyle velocity=Distance/Time$ so $\displaystyle Time=Distance/Speed$. Put the numbers in and you get the total time. Then you can work out how many 30 minute intervals there are and add 20 mins for each of them. All you have to do then is to subract the time from 4pm to get the starting time.

Hope it helps! - Jan 5th 2012, 08:45 AMokokjaeRe: Time algebraic question.
Here we go.

Distance = D = 60km

Rate = R = 20km per hour

Every 30 minutes, the boy travels 10km. [If he travels 20km per hour, half of that is 10km.]

This means, the boy must make 6 bike trips of 30 minutes. This also means, there are 5 breaks in-between of 20 minutes.

His trip looked like.. 30 bike, 20 rest, 30 bike, 20 rest, 30 bike, 20 rest, 30 bike, 20 rest, 30 bike, 20 rest, 30 bike.

Of.. he biked 6 times, rested 5 times.

6 x 30 = 180 minutes.

5 x 20 = 100 minutes.

His journey was for 380 minutes.

380 minutes / (1 hour/60 minutes) = X ammount of hours.

You take this number subtract by 4 pm and you have your answer. - Jan 5th 2012, 10:30 PMNickod777Re: Time algebraic question.
- Jan 7th 2012, 05:28 AMMathBondRe: Time algebraic question.
Thanks.