Respuesta :
Answer:
[tex]\text{Carol's 78 mph, Steve's 84 mph}[/tex]
Step-by-step explanation:
GIVEN: Steve and Carol live [tex]405[/tex] miles apart. They start at the same time and travel toward each other. Steve's speed is [tex]6\text{ mph}[/tex] greater than Carol's. If they meet in [tex]2.5\text{ hours}[/tex] , find their speeds.
TO FIND: find their speeds.
SOLUTION:
Distance between Steve and Carol [tex]=405\text{ miles}[/tex]
Let the speed of Carol be [tex]s[/tex]
As Steve's speed is [tex]6\text{ mph}[/tex] greater than Carol's.
Speed of Steve [tex]=s+6\text{ mph}[/tex]
As both are approaching towards each other
relative speed of Steve and Carol [tex]=\text{speed of Carol}+\text{speed of Steve}[/tex]
[tex]=(s)+(s+6)=2s+6[/tex]
Total time taken by both to meet each other [tex]=2.5\text{ hours}[/tex]
Total time taken by both to meet each other [tex]=\frac{\text{total distance}}{\text{relative speed of both}}[/tex]
[tex]=\frac{405}{2s+6}=2.5[/tex]
[tex]=5s+15=405[/tex]
[tex]5s=390[/tex]
[tex]s=78\text{ mph}[/tex]
speed of Carol [tex]=78\text{ mph}[/tex]
Speed of Steve [tex]=s+6=78+6=84\text{ mph}[/tex]
Hence the speed of Carol and Steve are [tex]78\text{ mph}[/tex] and [tex]84\text{ mph}[/tex] respectively
