Question

Steve and Carol live 405 miles apart. They start at the same time and travel toward each other. Steve's speed is 6mph greater than Carol's. If they meet in 2.5 hours, find their speeds.

Answer 1

`\text{Carol's 78 mph, Steve's 84 mph}`

Explanation:

GIVEN: Steve and Carol live
`405` miles apart. They start at the same time and travel toward each other. Steve's speed is
`6\text{ mph}` greater than Carol's. If they meet in
`2.5\text{ hours}` , find their speeds.

TO FIND: find their speeds.

SOLUTION:

Distance between Steve and Carol
`=405\text{ miles}`

Let the speed of Carol be
`s`

As Steve's speed is
`6\text{ mph}` greater than Carol's.

Speed of Steve
`=s+6\text{ mph}`

As both are approaching towards each other

relative speed of Steve and Carol
`=\text{speed of Carol}+\text{speed of Steve}`

`=(s)+(s+6)=2s+6`

Total time taken by both to meet each other
`=2.5\text{ hours}`

Total time taken by both to meet each other
`=\frac{\text{total distance}}{\text{relative speed of both}}`

`=(405)/(2s+6)=2.5`

`=5s+15=405`

`5s=390`

`s=78\text{ mph}`

speed of Carol
`=78\text{ mph}`

Speed of Steve
`=s+6=78+6=84\text{ mph}`

Hence the speed of Carol and Steve are
`78\text{ mph}` and
`84\text{ mph}` respectively