Question

Alvin runs 2 km to the bus stop, and then rides 4.5 km to school. On average, the bus is 45 km/h faster than Alvin’s average running speed. If the entire trip takes 25 min, how fast does Alvin run?

Answer 1

Given

Alvin runs 2 km to the bus stop, and then rides 4.5 km to school.

the bus is 45 km/h faster than Alvin’s average running speed

entire trip takes 25 min,

Find

how fast does Alvin run?

Step-by-step explanation

Let r be the running speed of Alvin

so , bus speed = 45 + r

time = distance/speed

run time + ride time = entire time

so ,

`\begin{gathered} (2)/(r)+(4.5)/(45+r)=(25)/(60) \\ \\ (2(45+r)+4.5r)/(r(45+r))=(5)/(12) \\ \end{gathered}`

on solving this , we get

`\begin{gathered} 5r^2+147r-1080=0 \\ r=6.0868,-35.48677 \end{gathered}`

as we neglect the negative value ,

so , r = 6.0868

Final Answer

Hence , the Alvin speed = 6.0868 approx