Question

Each of two cars, whose average rates are in the ratio of 4:5, travels the distance of 160 miles. If the fast car travels 1 2 an hour less than the slow car, find the average rate of each car.

Answer 1

64mph and 80 mph

Explanation:

let
`t_1,\ t_2 \ \ \ and \ v_1,\ v_2` be the time and speeds of the two cars in the 160 miles distance.

-Let v represent the speed values:

`v_1:v_2=4v:5v`

We are given that the fast car travels 0.5hr less than the slow car, thus:

`t_1=t\\\\t_2=t-0.5`

#We equate the two equations:

`d=vt\\\\\therefore 4vt=5v(t-0.5)\\\\4t=5(t-0.5)\\\\0.8t=t-0.5\\\\t=2.5`

#We substitute the value of t in the speed equation to find each cars speed:

`v_1=>160=vt\\\\v=(160)/(2.5)\\\\v_1=64 \ mph\\\\\\v_2=>160=vt\\\\\\`

`v=(160)/(2.5-0.5)\\\\v_2=80 \ mph\\`

The speed of the cars are 64mph and 80 mph