Question

Greg drove at a constant speed in a rainstorm for 250 miles. He took a​ break, and the rain stopped He then drove 159 miles at a speed that was 3 miles per hour faster than his previous speed. If he drove for 8 ​hours, find the​ car's speed for each part of the trip.

Answer 1

Speed during first part of the trip = 50 miles/hour

Speed during second part of trip = 53 miles/hour

Explanation:

Given:

Distance driven in rainstorm = 250 miles

Distance driven after rain stopped = 159 miles

Speed driven after rain stopped is 3 miles faster than the speed driven in rainstorm.

Total time driven = 8 hours

To find the speed of the car at each part of the trip.

Solution:

There are two parts of the trip.

1) Car driven in rainstorm:

Let the speed of the car during this part in miles/hour be =
`x`

Distance covered in this part = 250 miles.

Time taken in this trip =
`(Distance)/(Speed)=(250\ miles)/(x\ miles/hour)=(250)/(x)\ hours`

2) Car driven after rain stopped:

Speed of the car during this part in miles/hour will be =
`x+3`

Distance covered in this part = 159 miles.

Time taken in this trip =
`(Distance)/(Speed)=(159\ miles)/((x+3)\ miles/hour)=(159)/(x+3)\ hours`

Total time driven can be given as:

`(250)/(x) +(159)/(x+3) = 8`

Solving for
`x`.

Taking LCD.

`(250(x+3))/(x(x+3))+(159x)/(x(x+3))=8`

Simplifying.

`(250x+750+159x)/(x^2+3x)=8`

`(409x+750)/(x^2+3x)=8`

Multiplying both sides by
`(x^2+3x)`

`(x^2+3x)(409x+750)/(x^2+3x)=8(x^2+3x)`

`409x+750=8x^2+24x`

Subtracting both sides by 750.

`409x+750-750=8x^2+24x-750`

`409x=8x^2+24x-750`

Subtracting both sides by
`409x`

`409x-409x=8x^2+24x-409x-750`

`0=8x^2-385x-750`

Applying quadratic formula.

`x=(-b\pm√(b^2-4ac))/(2a)`

`x=(-(-385)\pm√((-385)^2-4(8)(-750)))/(2(8))`

`x=(385\pm415)/(16)`

`x=(385+415)/(16)` and
`x=(385-415)/(16)`

∴
`x=50` and
`x=-1.875`

Since speed cannot be taken as negative, so our solution will be 50 miles per hour.

Speed during first part of the trip = 50 miles/hour

Speed during second part of trip =
`50+3` = 53 miles/hour