At what time will Ted overtake John?

Question

John sets out for camp at 9:00 a.m. and walks 4 miles an hour. Ted sets out for camp at 9:30 a.m. and walks 5 miles per hour. At what time will Ted overtake John?

Answer 1

In the half hour between John starting and Ted starting, John has walked 2 miles.

So in time t (t = 0 when Ted starts) John walks 4t + 2 and Ted walks 5t

4t + 2 = 5t
t = 2

Ted will overtake after 2 hours i.e. at 11:30 a.m.

You could also approach this by saying John is 2 miles ahead when Ted starts. Ted is walking 1mph quicker, so will close the gap by 1 mile each hour. A two mile gap will therefore take 2 hours to close.

9:30 + 2 hours = 11:30 a.m.

Answer 2

Use the formula d = rt
(d = distance, r = rate, t = time)
We know that both went the same distance, d.
Then John's time is d/4 and Ted's it d/5.
Because Ted travelled 1/2 hour less than Ted
we must add 1/2 hour to his time to get John's.
So d/4 = d/5 + 1/2.
d/20 = 1/2
d = 10.
Thus John's time was 2.5 hours and Ted's was 2.
They will meet at 11.30 a.m.

Answer 3

11:30

Answer 4

11:30

Answer 5

John
9:30 am-----2 miles
10:30am-----6 miles
11:30am-----10 miles

Ted
9:30 am-----0 miles
10:30am-----5 miles
11:30am-----10 miles


So Ted will overtake John at 11:30am

Answer 6

To solve this, you have to write an equation for each person's location as a function of time:
J = 4*(t-9) ( this means time minus 9 AM)
T = 5*(t-9.5)

Then solve for when J = t, or
4*(t-9) = 5*(t-9.5)
4t-36 = 5t-9.5*5
5t-4t = 9.5*5 - 36
t = 9.5*5 - 36 = 11.5 = 11:30 AM