Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-Dave can hike on level ground 3 miles an hour faster than he can on uphill terrain. Yesterday, he hiked 30 miles, spending 2 hours on level ground and 5 hours on uphill terrain. Find his average speed on level ground.
A) 4.3 mph
B) 3.4 mph
C) 6.9 mph
D) 6.4 mph

Question

Quizplus · Accepted Answer

Let the speed of Dave on uphill terrain be $x$ mph. Therefore, his speed on level ground is $x + 3$ mph. The total distance covered is given by the sum of distances covered on level ground and uphill, which can be represented as $2(x + 3) + 5x = 30$. Solving this equation for $x$, we get $2x + 6 + 5x = 30$, which simplifies to $7x + 6 = 30$, and further to $7x = 24$, giving $x = \frac{24}{7}$ mph for uphill. For level ground, the speed is $x + 3 = \frac{24}{7} + 3 = \frac{24 + 21}{7} = \frac{45}{7} = 6.4$ mph.

Set Up an Equation That Can Be Used to Solve