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A passenger train leaves a train depot \(2 \mathrm{h}\) after a freight train leaves the same depot. The freight train is traveling 20 mph slower than the passenger train. Find the rate of each train if the passenger train overtakes the freight train in \(3 \mathrm{h}\).

For Exercises 38 to \(58,\) solve and check. $$5 x+2(x+1)=23$$

Solve and check. $$8 b-3=-9$$

A race car driver starts along a 50 -mile race course traveling at an average speed of \(90 \mathrm{mph}\). Fifteen minutes later, a second driver starts along the same course at an average speed of 120 mph. Will the second car overtake the first car before the drivers reach the end of the course?

A bus traveling at a rate of 60 mph overtakes a car traveling at a rate of 45 mph. If the car had a 1 -hour head start, how far from the starting point does the bus overtake the car?

A truck leaves a depot at 11 A.M. and travels at a speed of 45 mph. At noon, a van leaves the same depot and travels the same route at a speed of 65 mph. At what time does the van overtake the truck?

For Exercises 38 to \(58,\) solve and check. $$3[2-4(y-1)]=3(2 y+8)$$

A car travels a 1 -mile track at an average speed of 30 mph. At what average speed must the car travel the next mile so that the average speed for the \(2 \mathrm{mi}\) is \(60 \mathrm{mph}\) ?

Taxi Fares The fare \(F\) to be charged a customer by a taxi company is calculated using the formula \(F=2.50+2.30(m-1),\) where \(m\) is the number of miles traveled. Use this formula for Exercises 61 and 62 . A customer is charged \(\$ 14.00 .\) How many miles was the customer driven?

Taxi Fares The fare \(F\) to be charged a customer by a taxi company is calculated using the formula \(F=2.50+2.30(m-1),\) where \(m\) is the number of miles traveled. Use this formula for Exercises 61 and 62 . A passenger is charged \(\$ 20.90 .\) Find the number of miles the passenger was driven.