A car travels miles in hours at a constant speed. At this speed, how many miles will the car travel in hours?
For constant-speed word problems, quickly turn the information into a unit rate: divide distance by time to get miles per hour. Then multiply that rate by the new time to find the new distance. As a check, make sure your answer scales in the right direction—if time increases, distance at a constant speed must also increase—and avoid simply doubling or tripling numbers without first finding the correct rate.
Hints
Think about speed (rate)
You are told the car travels 150 miles in 3 hours at a constant speed. How can you find how many miles it travels in 1 hour?
Use the unit rate
Once you know how many miles the car goes in 1 hour, how can you use that to find how many miles it goes in 5 hours?
Set up an equation or proportion
You can either multiply the miles-per-hour rate by 5, or set up a proportion like and solve for , the distance in 5 hours.
Desmos Guide
Use Desmos to compute the new distance
In Desmos, type the expression (150/3)*5. The value that Desmos outputs is the number of miles the car will travel in 5 hours at the same constant speed.
Step-by-step Explanation
Find the car’s constant speed
The car goes 150 miles in 3 hours at a constant speed.
Speed (miles per hour) is distance ÷ time:
.
So the car’s speed is miles per hour.
Set up the distance for 5 hours
At the same constant speed, distance equals speed × time.
For 5 hours, the distance will be
miles.
Do not multiply yet if you want to check that the setup makes sense: more hours at the same positive speed should give a larger distance than 150 miles.
Calculate the distance and choose the answer
Now multiply to find the distance in 5 hours:
.
So the car will travel 250 miles in 5 hours, which corresponds to answer choice B.