Hanna is 124 miles away from Emily. They are traveling towards each other. If Emily travels 5 mph faster than Hanna and they meet after 4 hours, how fast was each traveling?

Question



Answer 1

This is a rate/distance/time question. Any time we want to calculate distance over time at a particular rate we use the formula: Distance = Rate x Time or D = RT

We can set this problem up in an algebraic equation with 124 miles being the combined distance that they both traveled. We will just use H for Hanna's speed of travel. Emily's speed is H+5. They each traveled 4 hours.

4H + 4(H+5) = 124 This is the complete equation

4H + 4H + 20 = 124 multiply 4 with the contents inside the parenthesis

8H + 20 = 124 combine like elements

8H = 104 subtract 20 from both sides

H = 13 divide both sides by 8 to get Hanna's speed

E = H + 5 = 18 Since Emily's speed is 5 more than Hanna's speed we just add 5.

Emily's speed was 18 MPH

Hanna's speed was 13 MPH