Answer:
3mph and 12mph
Step-by-step explanation:
GIVEN: Charlie biked [tex]15[/tex] minutes home from school and then walked [tex]12[/tex] minutes to the pizza place near his house. This trip was [tex]3.6[/tex] miles in total. His rate on his bike is [tex]3[/tex] miles per hour less than [tex]5[/tex] times his walking rate. In miles per hour.
TO FIND: Charlie’s speed as he walks and his speed as he bikes.
SOLUTION:
Let speed of charlie when he walks be [tex]x\text{ mph}[/tex]
Then speed of charlie as he biked [tex]=5x-3\text{ mph}[/tex]
Total length of trip [tex]=3.6\text{ miles}[/tex]
Total time taken[tex]=27\text{ minutes}=\frac{27}{60}\text{ hour}=\frac{9}{20}\text{hour}[/tex]
Now,
[tex]\text{Distance}=\text{speed}\times\text{time}[/tex]
distance traveled on bike [tex]=(5x-3)\times\frac{15}{60}=\frac{(5x-3)}{4}[/tex]
distance traveled by walking [tex]=x\times\frac{12}{60}=\frac{x}{5}[/tex]
As, [tex]\frac{(5x-3)}{4}+\frac{x}{5}=3.6[/tex]
[tex]\frac{29x-15}{20}=3.6\implies 29x=87[/tex]
[tex]\implies x=3\text{ mph}[/tex]
Speed of Charlie on bike [tex]=5x-3=12\text{ mph}[/tex]
Hence speed of charlie on bike and by walking is 12mph and 3mph respectively