Sarah travels from City A to City B at a speed of 50 mph and returns by the same route at a speed of 60 mph. If the total travel time is 7 hours, what is the distance between the two cities?
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Let the distance between the two cities be D.
The time taken to travel from city A to city B at a speed of 50 mph is D/50.
The time taken to travel from city B to city A at a speed of 60 mph is D/60.
According to the problem, the total travel time is 7 hours. So we have the equation:
D/50 + D/60 = 7
To simplify this equation, we can find a common denominator:
(60*D + 50*D)/ (50*60) = 7
Combining like terms in the numerator:
110*D/ (50*60) = 7
Multiplying both sides of the equation by (50*60) to isolate D:
110*D = 7 * (50*60)
Simplifying the right side of the equation:
110*D = 7 * 3000
Dividing both sides of the equation by 110 to solve for D:
D = (7*3000) / 110
D = 21000 / 110
D = 190.91
Therefore, the distance between the two cities is approximately 190.91 miles.
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