In a 100 m race, Harry the hare beats Terry the tortoise by 20 m.

Question

If terry starts 250 metres ahead, how much further will he reach before Harry catches him?

Answer 1

Harry beats Terry by 20 meters in a 100 meter race

if Terry has a head start of 250 meters, how far will Terry get before Harry catches up to him?

distance = time times rate of speed

d = rt

Let H= Harry's speed, and T = Terry's speed

100 = Ht

80 = Tt

Ht/Tt = 100/80

H/T = 10/8 = 5/4 = 1.25

H=1.25T

Harry "runs" 1 1/4 times as fast as Terry

d=rt

d/r = t

(250+x)/H = x/T

(250+x)/1.25T = x/T

(250+x)/1.25 = x

250+x = 1.25x

.25x = 250

x = 250/.25 = 1000 meters to catch up to Terry

Terry goes another 1000 meters as Harry goes 1250 meters