Question

The​ time, t, required to drive a fixed distance varies inversely as the​ speed, r. It takes 3 hr at a speed of 14 ​km/h to drive a fixed distance. How long will it take to drive the same distance at a speed of 23 ​km/h?

Answer 1

time taken with speed 23 km/h will be 1.8 hours or 1 hour 48 minutes

Step-by-step explanation:

Given:

Time is inversely proportional to the speed

mathematically,

t ∝ (1/r)

let the proportionality constant be 'k'

thus,

t = k/r

therefore, for case 1

time = 3 hr

speed = 14 km/hr

3 = k/14

also,

for case 2

let the time be = t

r = 23 km/h

thus,

we have

t = k/23

on dividing equation 2 by 1

we get

`(t)/(3)=(k/23)/(k/14)`

or

`t=(14*3)/(23)`

or

t = 1.8 hr = or 1 hour 48 minutes ( 0.8 hours × 60 minutes/hour = 48 minutes)