The Problem
Truck A can serve a full lunch to 160 people in 4 hours.
Truck B can serve the same number of people in 2.5 hours.
If they work together (at full speed), how long will it take them to serve 160 people?
Stretch my thinking...
What if there were 200 people? What about 500?
Student Solutions
See how our brilliant students approached this problem
Emma Chen
Solution Approach:
First I found how many people each truck serves per hour. Truck A serves 160 ÷ 4 = 40 people per hour. Truck B serves 160 ÷ 2.5 = 64 people per hour. Together they serve 40 + 64 = 104 people per hour. So for 160 people: 160 ÷ 104 = about 1.54 hours or 1 hour and 32 minutes. For 200 people: 200 ÷ 104 = about 1.92 hours. For 500 people: 500 ÷ 104 = about 4.81 hours.
Marcus Johnson
Solution Approach:
I used fractions to solve this. Truck A does 1/4 of the job per hour (because it takes 4 hours total). Truck B does 1/2.5 = 2/5 of the job per hour. Together: 1/4 + 2/5 = 5/20 + 8/20 = 13/20 of the job per hour. So they finish in 20/13 hours = about 1.54 hours for 160 people. I can use the same rate for other amounts.
Sophia Rodriguez
Solution Approach:
I made a table showing how many people each truck serves every 30 minutes. Truck A serves 20 people every 30 min, Truck B serves 32 people every 30 min. Together that's 52 people every 30 minutes. For 160 people: 160 ÷ 52 = about 3 periods of 30 minutes, so 1.5 hours. Then I calculated for 200 and 500 people the same way.
Group
Solution Approach:
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Working Out:
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