Question

Emma started biking to the coffee shop traveling 15 mph, after some time the bike got a flat so Emma walked the rest of the way, traveling 7 mph. If the total trip to the coffee shop took 9 hours and it was 103 miles away, how long did Emma travel at each speed

Answer 1

`75\text{ miles, }28\text{ miles}`

Explanation:

GIVEN: Emma started biking to the coffee shop traveling
`15 \text{mph}`, after some time the bike got a flat so Emma walked the rest of the way, traveling
`7 \text{mph}` If the total trip to the coffee shop took
`9 \text{hours}` and it was
`103 \text{miles}` away.

TO FIND: how long did Emma travel at each speed.

SOLUTION:

Let the distance traveled by Emma through bike is
`\text{x}`

Total time taken when traveled by bike
`=\frac{\text{x}}{15}`

Distance traveled through feet
`=103-\text{x}`

Total time taken when traveled by feet
`=\frac{103-\text{x}}{7}`

Now,

Total time taken
`=9\text{hours}`

`\frac{\text{x}}{15}+\frac{103-\text{x}}{7}=9`

`8\text{x}=600`

`\text{x}=75`

Distance traveled through feet
`=103-75=28\text{miles}`

Hence distance traveled using bike is
`75\text{miles}` and by feet is
`28\text{miles}`