Question

Samir begins riding his bike at a rate of 6 mph. Twelve minutes later, Chris leaves from the same point and bikes along the same route at 9 mph. At any given time, t, the distance traveled can be calculated using the formula d = rt, where d represents distance and r represents rate. How long after Chris begins riding does he catch up to Samir? 4 min 12 min 24 min 40 min

Answer 1

The correct answer option is 24 min.

Explanation:

Let us assume t to be Chris's time (in hours) so we can write the following equation:

Samir's time (in hours)
`=t + (12)/(60) = t + 0.2`

Chris's rate
`(r_1)=9 mph`

Samir's rate
`(r_2)=6 mph`

Then putting the values in the formula to get:

`r_1t = r_2(t + 0.2)`

`9t = 6(t + 0.2)`

`9t=6(t+0.2)\\\\9t=6t+1.2\\\\9t-6t=1.2\\\\3t=1.2\\\\t=0.4`

t = 0.4 which will be
`0.4*60=24`

Therefore, Chris catches up Samir after riding for 24 minutes.