Time, Distance, Rate Problems

[MattP2651]

Hi everyone, I hope I'm posting this in the right category. I have 2 math problems that I cant figure out how to arrive at the correct answer. I'm also not able to use a calculator. I thought for these problems you would use the formula: distance = rate x time.

1. If a fire engine is traveling at 40 miles per hour to a fire that is 6 miles away, how long will it take for the fire engine to reach the fire?
The correct answer is 9 minutes.

So for this one 6 = 40 x T
6 = 40T and then divide by 40 but I guess thats not correct.

2. Firefighters have been dispatched to a warehouse fire that is 3.7 miles away. If the fire engine averages 45 miles per hour, how long will it take the fire engine to reach the warehouse fire?
Correct answer is 4.9, and once again I do not know how to arrive at this answer.

Any explanations and work shown would be greatly appreciated and thank you in advance for taking the time to answer and show your work!

 

[topsquark]

1. If a fire engine is traveling at 40 miles per hour to a fire that is 6 miles away, how long will it take for the fire engine to reach the fire?
The correct answer is 9 minutes.

So for this one 6 = 40 x T
6 = 40T and then divide by 40 but I guess thats not correct.

The equation for average speed is [imath]\overline{v} = \dfrac{D}{T}[/imath], so as you say [imath]D = \overline{v} T[/imath].

The speed here is constant so the average speed is equal to the constant speed. So 6 = 40T, again, as you say. But this T will come out in hours, not minutes. Did you remember to convert the answer to minutes?

2. Firefighters have been dispatched to a warehouse fire that is 3.7 miles away. If the fire engine averages 45 miles per hour, how long will it take the fire engine to reach the warehouse fire?
Correct answer is 4.9, and once again I do not know how to arrive at this answer.

These are Physics problems. Always always always look at the units involved. The reasoning is exactly the same as you did for the first problem. You mentioned that the correct answer is 4.9. But 4.9 what? At a guess, I'd say you have to convert the time to minutes again.

-Dan