Question

It takes Maria, traveling at 28mph, 45 minutes longer to go a certain distance than it takes Ricky traveling at 70mph. Find the distance traveled.

Answer 1

We have two persons, Maria and Ricky, that travel the same distance but at different speeds.

We have to find the distance.

We can express the distance as the speed times the time interval.

The speed of Maria is 25 mph.

The speed of Ricky is 70 mph.

We don't know the time it took any of them to complete the distance, but we know that the time it took Maria is 45 minutes longer than the time it took Ricky.

Then, as the distance is the same, and if we call "t" (in minutes) to the time it took Ricky to travel that distance, we can write:

`\begin{gathered} d_m=d_r \\ v_m*t_m=v_r*t_r \\ 28*((t+45))/(60)=70*(t)/(60) \end{gathered}`

As Ricky took t minutes to complete the distance, then the time it takes Maria to complete the distance is t + 45.

We divide both by 60 to express it in hours because the speed is expressed in miles per hour.

We then can solve for t as:

`\begin{gathered} 28*((t+45))/(60)=70*(t)/(60) \\ 28t+28*45=70t \\ 28t+1260=70t \\ 28t-70t=-1260 \\ -42t=-1260 \\ t=(1260)/(42) \\ t=30 \end{gathered}`

It took Ricky 30 minutes to travel the distance.

Then we can use this to calculate the distance (d) as:

`\begin{gathered} d=v*t \\ d=70\text{ mph}*30\text{ min}*\frac{1\text{ hour}}{60\text{ min}}=35\text{ miles} \end{gathered}`

Answer: the distance traveled is 35 miles.