Applications of Fractions
What types of application problems involve fractions you've worked with in this unit?
Work problems Mixture problems Motion problems
A freight train travels at 30 mph. If the freight train is 300 miles ahead of an express train traveling at 55 mph, how long will the express train take to overtake the freight train? If x represents the distance the train traveling 30 mph travels, then the train traveling 55 mph travels
x + 300 miles
A freight train travels at 30 mph. If the freight train is 300 miles ahead of an express train traveling at 55 mph, how long will the express train take to overtake the freight train? Which equation could be used to find the number of miles the trains will travel?
x÷30 = (x + 300)÷55
A freight train travels at 30 mph. If the freight train is 300 miles ahead of an express train traveling at 55 mph, how long will the express train take to overtake the freight train?
12 hours
Joe Fleet can jog at the rate of 8 mph. Ron Pack can hike carrying camping equipment at the rate of 4 mph. They leave from opposite ends of a 44-mile trail at the same time. How far does Ron travel if he has 15 minutes to set up camp before Joe arrives?
14 miles
A plane can travel 640 miles against the wind in the same time it can travel 800 miles with the wind. If the plane can fly 180 mph in calm air, what is the speed of the wind?
20 mph
John has a boat that will travel at the rate of 15 kph in still water. He can go upstream for 35 km in the same time it takes to go 140 km downstream. How fast is his boat traveling when he goes downstream?
24 kph
Roger Waters can scrape up just enough money to rent a canoe for 1 hour and 30 minutes. If he paddles out on a lake at 4 kph and returns at 2 kph, how far will he have paddled the canoe?
4 km
A light private plane can fly 120 mph in still air. Flying against the wind, the plane can fly 320 miles in the same time it requires to fly 640 miles with the wind. Find the rate of the wind.
40 mph
A light private plane can fly 120 mph in still air. Flying against the wind, the plane can fly 320 miles in the same time it requires to fly 640 miles with the wind. Find the rate of the wind. If w represents the rate of the wind, which expression represents the time it takes the plane to travel the 640 miles with the wind?
640/(120 + w)
A plane can travel 640 miles against the wind in the same time it can travel 800 miles with the wind. If the plane can fly 180 mph in calm air, what is the speed of the wind? If x represents the speed of the wind, which expression represents the time it takes for the plane to travel the 640 miles against the wind?
640/(180 - x)
A boy swims downstream 0.9 miles in the same amount of time that he can swim 0.6 miles upstream. If the rate of the current is 1.5 mph, how fast can he swim in still water?
7.5 mph
Roger Waters can scrape up just enough money to rent a canoe for 1 hour and 30 minutes. If he paddles out on a lake at 4 kph and returns at 2 kph, how far will he have paddled the canoe? Which of the following is a true statement based on this problem?
The distance paddled out is equal to the distance paddled returning.