Question

DaMarcus and Fabian live $23$miles apart and play soccer at a park between their homes. DaMarcus rode his bike for three-quarters of an hour and Fabian rode his bike for half an hour to get to the park. Fabian’s speed was six miles per hour faster than DaMarcus’ speed. Find the speed of both soccer players.

Short answer

The speed of DaMarcus is$16miles/hr$and the speed of Fabian is$22miles/hr$.

Step-by-step solution

Step 1. Given Information.

Distance$=23miles$.

Time rode by DaMarcus$=\frac{3}{4}hours$.

Time rode by Fabian$=\frac{1}{2}hours$.$=23miles$

Step 2. Assumptions

Let the speed of DaMarcus be $xmiles/hr$.

Then, the speed of Fabian is $(x+6)miles/hr$.

We know, $Speed=\frac{Dis\tan ce}{Time}$.

Distance traveled by DaMarcusrole="math" localid="1647112289012" $=\frac{3x}{4}hours$.

Distance traveled by Fabian$=\frac{1}{2}(x+6)hours$.

Step 3. Solving the equations.

The equation according to the problem is,

$$\begin{gathered} \frac{3x}{4}+\frac{1}{2}(x+6)=23 \\ \frac{3x}{4}+\frac{x}{2}+3=23 \\ \frac{3x+2x}{4}=23-3 \\ \frac{5x}{4}=20 \\ x=20\times \frac{4}{5} \\ x=16 \end{gathered}$$

The speed of DaMarcus is $16miles/hr$.

$$\begin{gathered} x+6=16+6 \\ =22 \end{gathered}$$

The speed of Fabian is$22miles/hr$.