Grade 11 Math Problem: Solving for Distance and Time on a Family Road Trip

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A family traveled 880 km in 10 hours, with speeds of 100 km/h on highways and 60 km/h on city roads. The equations to solve for the time spent on each road type are 100x + 60y = 880 and x + y = 10. Substitution or elimination methods can be used to find the values of x (highway time) and y (city time). The correct solution indicates they spent 3 hours on highways and 7 hours on city roads. The discussion emphasizes collaborative problem-solving and sharing knowledge among participants.
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I have a question, a huge one but simply it is.. A family goes on a ten hour drive, 100km an hour on highways(x) and 60km(y) an hour on city roads.
100x+60y+880, and
x+y=10

Just need a push in the right direction. Thanks in advance.
 
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By the way, I have to find the hours in which they drove on each road type.
 
what is the question?
 
Did you really mean 100x+60y=880? If so, what you have are 2 equations in 2 unknowns. Have you covered how to solve these types of problems?
 
The bastow family drove to visit relatives. They drove a total of 880km in 10 hours. Their average speed was 100km on highways and 60km in the city. Let the time traveling on highways be "x" hours and the time on city roads be "y" hours. An equation that represents the total difference traveled is 100x+60y=880. An equation that represents the total traveling time is x+y=10.
a) What time was spent traveling highways?
b) What time was spent traveling city roads?
 
yah, 100x+60y=880, sorry about that.
 
We were taught substitution.
 
There you go!
 
i don't exactly remeber you could try it this way tho
take the second equation multipy iy by 100 so that x will be it will be 100x+100y=1000 put that direclty below the second equation subtract u will be left with 0 for the x then solve for y then plug y abck into the equation

sumone correct me if I am wrong because I am not sure if it works for that type of problem but i use that in geometry.
you cna alwyas try and cehck the answers in the book
 
  • #10
Oh man, jeeze, I can't believe I forgot that, thanks so much! :) You've both helped a heck of a lot!
 
  • #11
The final answer is (3,7)
 
  • #12
i can't help but feel that i ahve made a difference in sumone elses life today
 
  • #13
lmao, you sure have:D
 
  • #14
I'll pass the favor on tommorow:) Keep the chain going.
 

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