I have tried and tried to solve this problem, word problems just aren't my thing. Please help me!
In a 16 km cross-country ski race, Bob skied the first 7 km at a constant speed and then increased his speed by 3 km/hr for the last 9 km. If he finished the entire race in 1 h 20 min, what was his speed for the first 7 km?
Oh, and the answer is supposed to be 10.5 km/hr, i am just unsure of what i am doing wrong and why i am not getting this answer. Any help would be greatly appreciated! Thanks! :)
In a 16 km cross-country ski race, Bob skied the first 7 km at a constant speed and then increased his speed by 3 km/hr for the last 9 km. If he finished the entire race in 1 h 20 min, what was his speed for the first 7 km?
Oh, and the answer is supposed to be 10.5 km/hr, i am just unsure of what i am doing wrong and why i am not getting this answer. Any help would be greatly appreciated! Thanks! :)
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I used to have issues with word problems, you just have to read the numbers mostly and turn it into a "normal" math problem.
So for this you know the race is 16 km. You know he did the first 7 km at a constant speed. We can call the constant speed X. We don't know how long it took for him to finish the 7 km, we call this amount of time Y. So speed (km/hr) multiplied by the time (hours) = 7 or X*Y=7
He did the last 9 km at speed of X+3. Time for the 9 km we can call Z, so we have the 2nd part of the race (X+3)*Z=9.
You know it took 1 hr 20 mins. or (4/3 hours). So time for 7 km which is Y and the time for the 9 km which is Z, can combine to get Y+Z=(4/3)
So take all 3 equations you have:
X*Y=7
(X+3)*Z=9.
Y+Z=(4/3)
So now you have 3 equations and 3 unknowns. This shouldn't be too difficult to solve.
I did this too but I haven't done this in a while so may have taken the long way. I cut some steps and put .... when I did
Y+Z=(4/3) Z=4/3-Y
Plug in Z for 2nd equation, you get (X+3)*Z=9 OR XZ+3Z=9 OR X(4/3-Y) +3(4/3-Y)=9 .... Y=(5-4/3X)/(-X-3)
Plug in Y for first equation, you get X((5-4/3X)/(-X-3))=7......X=-1.5 OR X=10.5 since X is positive, you know it's 10.5 and not -1.5
So for this you know the race is 16 km. You know he did the first 7 km at a constant speed. We can call the constant speed X. We don't know how long it took for him to finish the 7 km, we call this amount of time Y. So speed (km/hr) multiplied by the time (hours) = 7 or X*Y=7
He did the last 9 km at speed of X+3. Time for the 9 km we can call Z, so we have the 2nd part of the race (X+3)*Z=9.
You know it took 1 hr 20 mins. or (4/3 hours). So time for 7 km which is Y and the time for the 9 km which is Z, can combine to get Y+Z=(4/3)
So take all 3 equations you have:
X*Y=7
(X+3)*Z=9.
Y+Z=(4/3)
So now you have 3 equations and 3 unknowns. This shouldn't be too difficult to solve.
I did this too but I haven't done this in a while so may have taken the long way. I cut some steps and put .... when I did
Y+Z=(4/3) Z=4/3-Y
Plug in Z for 2nd equation, you get (X+3)*Z=9 OR XZ+3Z=9 OR X(4/3-Y) +3(4/3-Y)=9 .... Y=(5-4/3X)/(-X-3)
Plug in Y for first equation, you get X((5-4/3X)/(-X-3))=7......X=-1.5 OR X=10.5 since X is positive, you know it's 10.5 and not -1.5
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Am not sure the answer can be 10.5km/hr i have tried am getting 9.3km/hr.
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Yes. 10.5 km/hr is correct