Freddie cycles to work everyday. By what percentage would he have to increase his speed in order to reduce the journey time by 20%?

Answer 1

distance = rate of speed times time

d =rt

d=a constant, the same distance before or after a change in speed and time

r = d/t

pr = d/.8t with .8t = 20% decrease, p= percent change in rate of speed

.8tpr = d = rt

.8tpr = rt divide by rt

.8p = 1

p = 1/.8 = 1/8/10 = 10/8 = 5/4 = 1.25 which is a 25% increase in speed to get a 20% decrease in time

take a more specific example

he cycles 10 miles each day

he goes 5 mph arriving in 2 hours

he wants to decrease his time by 20% from 2 hours to 1.6 hours. 20% of 2 = .4. 2-.4 =1.6

10 = speed times time = 5(2)

10 = r(1.6)

r = 10/1.6 = 10/16/10 = 100/16 = 50/8 = 25/4 = 6.25

from 5 to 6.25 is an increase in speed of 1.25 mph

1.25/5 = 2.5/10 = .25 = 25% increase in speed to get a 20% reduction in time