Question

if a cyclist had gone 3 km per hour faster he would have taken 1 hour and 20 minutes less to ride 80km. what time did he take

Answer 1

Define x:

Let the original speed be x

Convert time to hours:

1 hour 20 mins = 4/3 hours

Find the time needed for original speed:

Time = Distance ÷ Speed

Time = 80/x

Find the time needed for the faster speed:

Given that the speed is 3 k/h faster

Time = Distance ÷ Speed

Time = 80/(x + 3)

Solve x:

The difference in time is 4/3 hour

80/x - 80/(x + 3) = 4/3

80(x + 3) - 80x = 4/3 (x)(x + 3)

80x + 240x - 80x = 4/3 x² + 4x

4/3 x² + 4x - 240 = 0

4x² + 12x - 720 = 0

x² + 3x - 180 = 0

(x - 12) (x + 15) = 0

x = 12 or x = -15 (rejected, because it is negative)

Find the original speed:

Original Speed = x = 12 km/h

Find the time he took:

Time = Distance ÷ Speed

Time = 80 ÷ 12 = 20/6 hours = 6 hours 40 mins

Answer: He took 6 hours 40 mins

Answer 2

hey!

here is answer

see in. pic

let original speed be x

change time in hour

we have to. use a formula of physics

Time= distance / speed

means distance ÷speed

we solve it for x

and answer will be

original speed = 12km/h

time= 20/3 hours