One car went 10 miles farther when traveling at 50 mph than a second car that traveled 2 hours longer at a speed of 40 mph. How long did the first car travel?
The correct answer and explanation is:
✅ Correct Answer: 5 hours
✍️ Explanation:
We are given:
- First car:
- Speed = 50 mph
- Distance = 10 miles more than the second car
- Second car:
- Speed = 40 mph
- Time = 2 hours more than the first car
Let’s let the time the first car traveled be:
x hours
Then, the time the second car traveled is:
x + 2 hours
Now, we use the distance formula: Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time}
So,
- Distance of first car = 50x50x
- Distance of second car = 40(x+2)40(x + 2)
We are told the first car traveled 10 miles farther: 50x=40(x+2)+1050x = 40(x + 2) + 10
🧮 Solve the equation:
Expand the right-hand side: 50x=40x+80+1050x = 40x + 80 + 10 50x=40x+9050x = 40x + 90
Subtract 40x from both sides: 10x=9010x = 90
Divide both sides by 10: x=9x = 9
Wait! That gives us x = 9, not 5. Let’s double-check.
Ah! There was a miscalculation. Let’s correct it from the equation step.
Actually, the correct equation should be: 50x=40(x+2)+1050x = 40(x + 2) + 10 50x=40x+80+1050x = 40x + 80 + 10 50x=40x+9050x = 40x + 90
Subtract 40x: 10x=90⇒x=910x = 90 \Rightarrow x = 9
✅ Corrected Answer: 9 hours
✅ Final Answer: 9 hours
So, the first car traveled for 9 hours, covering a distance of: 50×9=450 miles50 \times 9 = 450 \text{ miles}
And the second car traveled for: 9+2=11 hours⇒40×11=440 miles9 + 2 = 11 \text{ hours} \Rightarrow 40 \times 11 = 440 \text{ miles}
This confirms the first car went 10 miles farther than the second.