Question

2 cars raced at a track. the faster car traveled 20mph faster than the slower car. in the time that the slower car traveled 165 miles, the faster car traveled 225 miles. if the speeds of the cars remained constant, how fast did the slower car travel during the race.

Answer 1

The speed of slower car is 55 miles per hour.

Explanation:

Given as :

The speed of slower car =
`s_2` = s mph

The speed of faster car =
`s_1` = ( s + 20 ) mph

The distance cover by slower car =
`d_2` = 165 miles

The distance cover by faster car =
`d_1` = 225 miles

The time taken by both cars for travelling = t hours

The speed of the cars remains constant

Now, According to question

∵ Time =
`(\textrm Distance)/(\textrm Speed)`

So, For slower car

t =
`(d_2)/(s_2)`

Or, t =
`(165)/(s)` ............1

So, For faster car

t =
`(d_1)/(s_1)`

Or, t =
`(225)/(s+20)` ............2

Now, equating both the equations

I.e
`(225)/(s+20)` =
`(165)/(s)`

By cross multiplying

Or, 225 × s = 165 × (s + 20)

Or, 225 s = 165 s + 3300

Or, 225 s - 165 s = 3300

Or, 60 s = 3300

∴ s =
`(3300)/(60)`

I.e s = 55 miles per hour

So , The speed of slower car =
`s_2` = s = 55 miles per hour

Hence , The speed of slower car is 55 miles per hour. Answer