Answer:
[tex]75\text{ miles, }28\text{ miles}[/tex]
Step-by-step explanation:
GIVEN: Emma started biking to the coffee shop traveling [tex]15 \text{mph}[/tex], after some time the bike got a flat so Emma walked the rest of the way, traveling [tex]7 \text{mph}[/tex] If the total trip to the coffee shop took [tex]9 \text{hours}[/tex] and it was [tex]103 \text{miles}[/tex] away.
TO FIND: how long did Emma travel at each speed.
SOLUTION:
Let the distance traveled by Emma through bike is [tex]\text{x}[/tex]
Total time taken when traveled by bike [tex]=\frac{\text{x}}{15}[/tex]
Distance traveled through feet [tex]=103-\text{x}[/tex]
Total time taken when traveled by feet [tex]=\frac{103-\text{x}}{7}[/tex]
Now,
Total time taken [tex]=9\text{hours}[/tex]
[tex]\frac{\text{x}}{15}+\frac{103-\text{x}}{7}=9[/tex]
[tex]8\text{x}=600[/tex]
[tex]\text{x}=75[/tex]
Distance traveled through feet [tex]=103-75=28\text{miles}[/tex]
Hence distance traveled using bike is [tex]75\text{miles}[/tex] and by feet is [tex]28\text{miles}[/tex]
