Question

Ethan and Leo start riding their bikes at the opposite ends of a $65-$mile bike path. After Ethan has ridden $1.5$hours and Leo has ridden $2$hours, they meet on the path. Ethan’s speed is six miles per hour faster than Leo’s speed. Find the speed of the two bikers.

Short answer

The speed of Leo is $16miles/hr$and the speed of Ethan is$22miles/hr$.

Step-by-step solution

Step 1. Given Information.

Distance of bike-path$=65miles$.

Time rode by Ethan$=1.5hours$.

Time rode by Leorole="math" localid="1647110478618" $=2hours$.

Step 2. Assumptions.

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

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

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

Distance traveled by Leo is $2xmiles$.

Distance traveled by Ethan is$1.5(x+6)miles$.

Step 3. Solving the equations.

The equation according to the problem is,

$$\begin{gathered} 2x+1.5(x+6)=65 \\ 2x+1.5x+9=65 \\ 3.5x=56 \\ x=16 \end{gathered}$$

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

Now, role="math" localid="1647110849151" $$\begin{gathered} x+6=16+6 \\ =22 \end{gathered}$$

The speed of Ethan isrole="math" localid="1647110837569" $22miles/hr$.