Question

Mike leaves the house on a bike at 9am. Amy leaves 3 hours later, and goes 21km/h faster than Mike. If Amy overtakes Mike after 196km, what is average speed of both vehicles?

Answer 1

after 3 hours, at speed m, Mike has gone 3m km ahead.
The speed difference is 21 km/hr, so it will take Amy 3m/21 = m/7 hours to overtake Mike.
So, m/7 * (m+21) = 196
m = 28
So, the average speed is (28+(28+21))/2 = 38.5 km/hr

On the other hand, the weighted average (totaldistance/totaltime) is (7*28+4*49)/(7+4) = 35.6 km/hr
since more time was spent at the slower speed.

Answer 2

Thanks Steve, how do you know to divide your 3m by the difference in speed?

Answer 3

The difference is speed determines how long it will take for Amy to catch up. The rest of her speed is the same as Mike's, so she does not gain any distance except for the extra speed she has. Play with some simple numbers and you can see that this is so.

Answer 4

Ok great thanks!