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 [tex]=\dfrac{8}{x}[/tex] hours
William:
Distance = 12 miles
Speed = x mph
Time [tex]=\dfrac{12}{x}[/tex] hours
It 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 miles
Speed = 55 mph
Time [tex]=\dfrac{120}{55}=2\dfrac{10}{55}=2\dfrac{2}{11}\[/tex] hours
Final:
Speed = 44 mph
Time [tex]=2\dfrac{2}{11}[/tex] hours
Distance [tex]=44\cdot 2\dfrac{2}{11}=44\cdot \dfrac{24}{11}=4\cdot 24=96\ miles[/tex]
