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?

Explanation

Let r be the running speed of Alvin

so , bus speed = 45 + r

time = distance/speed

run time + ride time = entire time

so ,

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

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