If the speed is increased by 5 miles per hour, the trip would take one hour less time. What is the cars original speed?

Question

A car travels for 100 miles at a uniform speed. If the speed is increased by 5 miles per hour, the trip would take one hour less time. What is the cars original speed?

Answer 1

let the original time be t

 

100 = v*t ; giving t = 100/v

 

100 = (v+5)(t-1)

 

100 = (v+5)(100/v -1) = 100 - v +500/v - 5

 

v - 500/v + 5 = 0  multiply throughout by v

 

v² - 500 +5v = 0

 

v² + 5v - 500 = 0

 

(v-20)(v-25) = 0

 

v = 20 or -25

 

the negative sign has no practical significance

 

Henve v = 20 mph

 

checking; 100/20 = 5 hours, 100/25 = 4 hours, hence adding 5 mph to the speed shortens the journey by 1 hour