Question

Dona drove 300 miles north from San Antonio, mostly on the freeway. She usually averaged 55 mph, but an accident slowed her speed through Dallas to 15 mph. If her trip took 6 hours, how many miles did she drive at the reduced rate ?

Answer 1

The distance she took at reduce speed is 11.25 miles

Explanation:

Given as :

The Distance cover from San Antonio before accident = D miles

The Distance cover after accident = ( 300 - D ) miles

The average speed before accident = 55 mph

The average speed after accident = 15 mph

Total time for the journey = 6 hours

Now, Time =
`(Distane)/(Speed)`

∴
`(D)/(55)` +
`(D - 300)/(15)` = 6

Or,
`(3 D + 11 ( 300 - D ))/(165)` = 6

Or,
`(3 D + 3300 - 11 D)/(165)` = 6

Or, 3300 - 8 D = 165 × 6

Or, 3300 - 8 D = 990

Or, 8 D = 2310

∴ D =
`(2310)/(8)` = 288.75 miles

The distance travel at reduce speed = 300 - D

= 300 - 288.75

= 11.25 miles

Hence The distance she took at reduce speed is 11.25 miles