Question 17·Medium·Ratios, Rates, Proportional Relationships, and Units
A high-speed train travels at a constant speed of meters per second. At this speed, how many kilometers will the train travel in minutes?
(Express the answer as an integer)
For unit-rate and conversion problems, first make all units compatible with the given rate (here, convert minutes to seconds because the speed is in meters per second). Then apply the basic formula to find the quantity in the rate’s units, and finally convert that result into the units the question asks for. Keep track of units at each step and use the given conversion factor (like kilometer meters) to avoid common mistakes.
Hints
Match the time units to the speed units
The speed is in meters per second. Your time is given in minutes. What should you do so that the time and speed use compatible units?
Find the distance in meters first
After converting minutes to seconds, use the formula to find how many meters the train travels in that time.
Convert meters to kilometers
Once you have the distance in meters, remember that kilometer equals meters. How do you change meters into kilometers using this fact?
Desmos Guide
Enter a single expression for the distance in kilometers
In a Desmos expression line, type 150*4*60/1000. This expression multiplies the speed by the time in seconds and then divides by 1000 to convert meters to kilometers.
Read the numerical result
Look at the value Desmos displays to the right of the expression. That value is the number of kilometers the train travels in 4 minutes at 150 meters per second.
Step-by-step Explanation
Convert time from minutes to seconds
The speed is given in meters per second, so the time must be in seconds.
Convert minutes to seconds:
Use distance = speed × time to find meters traveled
Distance traveled at constant speed is
Here, speed meters per second and time seconds, so
The train travels meters in minutes.
Convert meters to kilometers
We are asked for the distance in kilometers, and we know that
So to convert meters to kilometers, divide by :
Compute the final value in kilometers
Now perform the division:
So, the train will travel 36 kilometers in minutes.