Question 1005061: A city bus finishes its 96 mile route in the same amount of time that a rural bus finishes its 144 mile route. The city bus averages 18 mph slower than the rural bus. How long does it take each bus to finish its route?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rate * time = distance.
city bus distance = 96 miles.
rural bus distance = 144 miles.
city bus rate = 18 mph less than the rural bus rate.
assume the rural bus rate is x miles per hour.
the city bus rate is therefore x - 18
for the city bus:
rate * time = distance becomes (x-18) * time = 96
for the rural bus:
rate * time = distance becomes x * time = 144
time is the same for both.
we'll solve each equation for time to get:
time = 96 / (x-18) for the city bus.
time = 144 / x for the rural bus.
we replace time in the second equation with the equivalent value for time in the first equation to get:
96 / (x-18) = 144 / x
we multiply both sides of the equation by (x-18) * x to get:
x * (x-18) * 96 / (x-18) = x * (x-18) * 144 / x
we simplify to get:
x * 96 = (x-18) * 144
we simplify further to get:
x * 96 = 144 * x - 18 * 144
we simplify further to get:
96x = 144x - 2592
we subtract 96x from both sides of this equation and add 2592 to both sides of this equation to get:
2592 = 144x - 96x
we simplify to get:
2592 = 48x
we divide both sides of this equation by 48 to get:
2592 / 48 = x
we solve for x to get:
x = 54
that's the rate of the rural bus.
the rate of the city bus is 18 mph less than that.
the rate of the city bus is 54 - 18 = 36 mph.
the rural bus travels at 54 mph.
the city bus travels at 36 mph.
if we did this correctly, time should be the same for both buses.
for the city bus, the formula is 36 * time = 96 miles
solve for time to get time = 96 / 36 = 8/3 hours.
for the rural bus, the formula is 54 * time = 144 miles
solve for time to get time = 144 / 54 = 8/3 hours.
time is the same for both so we're done.
they asked for how long each bus took to finish its route.
the solution is that each bus took 8/3 hours to finish its route.
this is equivalent to 2 and 2/3 hours.
as a bonus, we also figured out how fast each bus was traveling.
the city bus was traveling at 36 miles per hour.
the rural bus was traveling at 54 miles per hour.
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