Question

a car is traveling at a speed of either 55 miles per hour or 35 miles per hour, depending on the speed limits, until it reaches its destination 200 miles away.

• let x represent the amount of time, in hours, that the car is traveling at 55 miles per hour.
• let y represent the amount of time, in hours, that the car is traveling at 35 miles per hour.
• the equation ( 55x + 35y = 200 ) represents this situation.

if the car spends 2.5 hours traveling at 35 miles per hour on the trip, how long does it spend traveling at 55 miles per hour?

Explanation:

Step1: Substitute y=2.5 into equation

$55x + 35(2.5) = 200$

Step2: Calculate 35×2.5

$55x + 87.5 = 200$

Step3: Isolate 55x term

$55x = 200 - 87.5$
$55x = 112.5$

Step4: Solve for x

$x = \frac{112.5}{55}$
$x = \frac{225}{110} = \frac{45}{22} \approx 2.05$

Answer:

The car spends $\frac{45}{22}$ hours (approximately 2.05 hours) traveling at 55 miles per hour.