a. It spends about 2.045 hours going 55 miles per hour
b. It spends 1 hour going 35 miles per hour
c. The trip would take about 3.64 hours
Step-by-step explanation:
A car is traveling on a small highway and is either going 55 miles per hour or 35 miles per hour, depending on the speed limits, until it reaches its destination 200 miles away
- x represents the amount of time in hours that the car is going 55 miles per hour
- y represents the amount of time in hours that the car is going 35 miles per hour
- The equation that describing the relationship is 55x + 35y = 200
We need to find:
a. How long does it spend going 55 miles per hour, if the car spends 2.5 hours going 35 miles per hour on the trip
∵ 55x + 35y = 200
∵ The car spends 2.5 hours going 35 miles per hour on the trip
∵ y represents the amount of time that the car going 35 mi./h
∴ y = 2.5
- Substitute the value of y in the equation to find the value of x
∴ 55x + 35(2.5) = 200
∴ 55x + 87.5 = 200
- Subtract 87.5 from both sides
∴ 55x = 112.5
- Divide both sides by 55
∴ x = 2.045 hours
It spends about 2.045 hours going 55 miles per hour
b.how long does it spend going 35 miles per hour, if the car spends 3 hours going 55 miles per hour on the trip
∵ 55x + 35y = 200
∵ The car spends 3 hours going 55 miles per hour on the trip
∵ x represents the amount of time that the car going 55 mi./h
∴ x = 3
- Substitute the value of y in the equation to find the value of x
∴ 55(3) + 35y = 200
∴ 165 + 35y = 200
- Subtract 165 from both sides
∴ 35y = 35
- Divide both sides by 35
∴ y = 1 hour
It spends 1 hour going 35 miles per hour
c. How long would the trip take, if the car spends no time going 35 miles per hour
∵ 55x + 35y = 200
∵ The car spends no time going 35 miles per hour
∴ y = 0
- Substitute the value of y in the equation to find the value of x
∴ 55x + 35(0) = 200
∴ 55x = 200
- Divide both sides by 55
∴ x = 3.63 hours
The trip would take about 3.64 hours
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