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
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
Learn more:
You can learn more about the equations in brainly.com/question/4097107
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