Trouble setting up a quadratics problem involving distance, speed and time.

[Realtomcruise62]

I have been having problems setting up the following word problem, the actual quadratics is no problem to solve but I don’t know how to define the equation from the following:

“The Hockey Team are travelling from City A to City B, a distance of 730 km, on their Charter Bus. On the return trip, their average speed was increased by 10 km/h. If the total driving time for the round trip was 17 hours, determine their average speed on the trip from City A to City B.”

I’ve tried for about an hour to set it up using a chart to list my variables and find solutions to similar problems online to no avail. For whatever reason this form of question has never clicked for me. Any advice on how to set up similar velocity, distance time quadratic problems in general would be greatly appreciated as well, of all things I find these questions in particular the most confusing things I’ve done yet in maths lol. Thanks in advance.

 

[blamocur]

Let [imath]v[/imath] be the speed from A to B, then:

1. What is the travel time from A to B?
2. What is the speed from B to A ?
3. What is the travel time from B to A?
4. What is the total travel time expressed in terms of [imath]v[/imath]?

 

[Realtomcruise62]

Let [imath]v[/imath] be the speed from A to B, then:

1. What is the travel time from A to B?
2. What is the speed from B to A ?
3. What is the travel time from B to A?
4. What is the total travel time expressed in terms of [imath]v[/imath]?

Brilliant, it took me a bit before I realized how to do it, but looking back at my chart of values I set up prior made it all fall in place for me. Before I mark it solved however can someone confirm that the answer is 81.17…km/h? I was given as 81km/h on an answer key and I want to make absolute sure that it was a rounded value and not a minuscule mistake on my part.

Genuine thanks regardless, I’m not joking when I say the question was haunting me all day when I couldn’t figure out how to set up such a simple seeming word problem.

 

[Harry_the_cat]

I always set up a table for these distance, time, speed problems.

	A to B​	B to A​
Distance​	730​	730​
Time​
Speed​

That bit is given.

Now the question wants you to find the average speed from A to B. So let that be x km/h. (Always try to use one variable in the table only.)
You should now be able to fill in the "speed" row of the table in terms of x, using the info "On the return trip, their average speed was increased by 10 km/h." .

Knowing the relationship between distance, time and speed, you should now be able to fill in the "time" row in terms of x.

Lastly, using "the total driving time for the round trip was 17 hours", can you form the appropriate equation?

Then it's up to you to solve and interpret your answer.

Please show us what you have done.

 

[blamocur]

Before I mark it solved however can someone confirm that the answer is 81.17…km/h?

You answer looks good to me. In the future, there is a simple way to verify your equations: just plug in the solution into the equation. I.e.:
[math]\frac{730}{81.17} + \frac{730}{10 + 81.17} = ???[/math]

 

[Dr.Peterson]

Before I mark it solved however can someone confirm that the answer is 81.17…km/h? I was given as 81km/h on an answer key and I want to make absolute sure that it was a rounded value and not a minuscule mistake on my part.

If you want to check your answer, and are not entirely sure of the equation, I recommend checking the statements of the original problem, assuming your answer.

“The Hockey Team are travelling from City A to City B, a distance of 730 km, on their Charter Bus. On the return trip, their average speed was increased by 10 km/h. If the total driving time for the round trip was 17 hours, determine their average speed on the trip from City A to City B.”

So, suppose that their average speed on the trip from City A to City B is 81.17 km/h, and calculate the time from A to B and from B to A, to see if the total time is 17 hours (within reasonable rounding) as required. If it turned out that you were wrong, doing this, with specific numbers, might help you see where the equation should have been different.

You might also try checking their (rounded) answer, and confirm that it doesn't work better than your (less rounded) answer. That can help you see that the rounding is the only issue.