Question

1) Eliot and William went hiking. They went at the same speed. Eliot's hike was 8 miles, and William's hike was 12 miles. It took Eliot 40 min less than William. How long was William's hike?
2) During a certain period of time, a car can cover a distance of 120 miles, going at an average speed of 55 mph. What distance over the same period of time would cover a truck, going at an average speed of 44 mph?

THANK YOU SO MUCH!! PLEASE GIVE EXPLANATION!!! I WILL MARK BRAINLIEST!!

Answer 1

Answer:

1) 2 hours

2) 96 miles

Step-by-step explanation:

1) Eliot and William went hiking. They went at the same speed. Let x mph be their speed.

Elliot:

Distance = 8 miles

Speed = x mph

Time $=\dfrac{8}{x}$ hours

William:

Distance = 12 miles

Speed = x mph

Time $=\dfrac{12}{x}$ hours

It took Eliot $40\ min=\dfrac{40}{60}\ hour=\dfrac{2}{3}\ hour$ less than William, then

$\dfrac{8}{x}+\dfrac{2}{3}=\dfrac{12}{x}\\ \\\dfrac{2}{3}=\dfrac{12}{x}-\dfrac{8}{x}\\ \\\dfrac{2}{3}=\dfrac{4}{x}\\ \\2x=3\cdot 4\ \ [\text{Cross multiply}]\\ \\2x=12\\ \\x=6\ mph$

So, William's hike was

$\dfrac{12}{6}=2$

hours long.

2) Initially:

Distance = 120 miles

Speed = 55 mph

Time $=\dfrac{120}{55}=2\dfrac{10}{55}=2\dfrac{2}{11}$ hours

Final:

Speed = 44 mph

Time $=2\dfrac{2}{11}$ hours

Distance $=44\cdot 2\dfrac{2}{11}=44\cdot \dfrac{24}{11}=4\cdot 24=96\ miles$