MATH SOLVE

3 months ago

Q:
# 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!!

Accepted Solution

A:

Answer:1) 2 hours2) 96 milesStep-by-step explanation:1) Eliot and William went hiking. They went at the same speed. Let x mph be their speed.Elliot:Distance = 8 milesSpeed = x mphTime [tex]=\dfrac{8}{x}[/tex] hoursWilliam:Distance = 12 milesSpeed = x mphTime [tex]=\dfrac{12}{x}[/tex] hoursIt took Eliot [tex]40\ min=\dfrac{40}{60}\ hour=\dfrac{2}{3}\ hour[/tex] less than William, then[tex]\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[/tex]So, William's hike was [tex]\dfrac{12}{6}=2[/tex]hours long.2) Initially:Distance = 120 milesSpeed = 55 mphTime [tex]=\dfrac{120}{55}=2\dfrac{10}{55}=2\dfrac{2}{11}\[/tex] hoursFinal:Speed = 44 mphTime [tex]=2\dfrac{2}{11}[/tex] hoursDistance [tex]=44\cdot 2\dfrac{2}{11}=44\cdot \dfrac{24}{11}=4\cdot 24=96\ miles[/tex]