Answer :
The usual speed of the bus is 60 km/hr.
Define speed.
Speed is the rate of change in location of an item, expressed in meters per second.
Given,
Let x be the usual speed.
Speed = Distance/ Time
Time = Distance/Speed
Bus usually travels 350 miles.
It takes time for it to get there = 350/x h
The bus departs this week at 6:10, though.
The 70-minute bus delay = 70/60 = 7/6 h
The bus's current speed is (x+10) miles per hour.
The new window of time for getting there is [tex]\frac{350}{x+10}[/tex]
[tex]\frac{350}{x}[/tex] + [tex]\frac{350}{x+10}[/tex] = [tex]\frac{7}{6}[/tex]
350([tex]\frac{x+10-x}{x(x+10)}[/tex] ) = [tex]\frac{7}{6}[/tex]
350 ( [tex]\frac{10}{x^{2} +10x}[/tex] )= [tex]\frac{7}{6}[/tex]
7(x² +10x) = 6(350)(10)
x² + 10x = 3000
x² + 10x - 3000 = 0
x² -60x + 50x - 3000 = 0
x( x - 60) + 50(x - 60) = 0
(x + 50)(x - 60) = 0
x = -50 , x = 60
The usual speed of the bus is 60 km/hr.
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