Question

Mindy left at 8 a.m. and will arrive at 1.pm. Kelly left at 8a.m. and will arrive at 2p.m. How many miles is the trip of Kelly is traveling 10 miles per hour slower than Mindy ?

Answer 1

Mindy's time: 5 h

Kelly's time: 6 h

The distance is the same for both of them, then

`\begin{gathered} d=r_mt_m\text{ for Mandy} \\ d=r_kt_k\text{ for Kelly} \end{gathered}`
`\begin{gathered} r_mt_m=r_kt_k \\ r_m*5=(r_m-10)*6 \\ r_m*5=6r_m-60 \\ r_m=60\text{ mi/h} \end{gathered}`

for Kelly

`\begin{gathered} r_k=r_m-10 \\ r_k=60-10 \\ r_k=50\text{ mi/h} \end{gathered}`

so

`\begin{gathered} d=r_mt_m \\ d=60*5 \\ d=300\text{ }mi\text{ for Mandy} \end{gathered}`
`\begin{gathered} d=r_kt_k \\ d=50*6 \\ d=300\text{ mi for Kelly} \end{gathered}`

Both ways of finding d agree, so distance is 300 miles