QuestionA Jeep and BMW enter a highway running east-west at the same exit heading in opposite directions. The jeep entered the highway 30 minutes before the BMW did, and traveled 9 mph slower than the BMW. After 2 hours from the time the BMW entered the highway, the cars were 292.5 miles apart. Find the speed of each car, assuming they were driven on cruise control.
The Jeep was traveling at mph and the BMW was traveling at mph.
Studdy Solution
STEP 1
1. The Jeep and BMW are traveling in opposite directions.
2. The Jeep entered the highway 30 minutes (0.5 hours) before the BMW.
3. The Jeep travels 9 mph slower than the BMW.
4. After 2 hours from the time the BMW entered, they are 292.5 miles apart.
5. Both vehicles are on cruise control, meaning their speeds are constant.
STEP 2
1. Define variables for the speeds of the Jeep and BMW.
2. Express the relationship between the speeds of the Jeep and BMW.
3. Calculate the distance traveled by each vehicle.
4. Set up and solve the equation based on the total distance apart.
STEP 3
Define variables for the speeds of the Jeep and BMW.
Let be the speed of the BMW in mph.
Then, the speed of the Jeep is mph.
STEP 4
Express the relationship between the speeds of the Jeep and BMW.
Since the Jeep travels 9 mph slower than the BMW, we have:
STEP 5
Calculate the distance traveled by each vehicle.
The BMW travels for 2 hours, so the distance it travels is:
The Jeep travels for 2.5 hours (since it started 0.5 hours earlier), so the distance it travels is:
STEP 6
Set up and solve the equation based on the total distance apart.
The sum of the distances traveled by the Jeep and BMW is 292.5 miles:
Simplify and solve the equation:
Add 22.5 to both sides:
Divide both sides by 4.5:
The speed of the BMW is 70 mph.
STEP 7
Calculate the speed of the Jeep.
Since the Jeep travels 9 mph slower than the BMW:
The Jeep was traveling at mph and the BMW was traveling at mph.
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