Question 99972: In a walkathon to raise money for charity, Elisa walked a certain distance at 5 mi/h and then jogged twice that distance at 8 mi/h. Her total time walking and jogging was 2 h and 15 min. How many miles long was the walkathon?
Found 2 solutions by fastblue, TP:
Answer by fastblue(13)   (Show Source):
You can put this solution on YOUR website! The problem says she went twice as far jogging as she did walking so:
2*5*t=8*(2.25-t), where t is for time. Solving this equation tells you
how long she did both, then substitute back in for each speed to get total distance.
so 10t=18-8t, and 18t=18, so t=1 hour.
so (5*1)+(8*1.25)= total distance traveled = 15 miles which is the length of the walkathon.
Answer by TP(29) (Show Source):
You can put this solution on YOUR website! You will need to be able to use the formula: distance = speed*time.
Always give the unknowns appropriate labels. Here, since the journey is in two stages, two different times are involved and we will need to find their values before we can find the total distance.
Call them T(time taken for 1st stage) and t(time taken for 2nd stage).
Units: Since the speeds are given in miles per hour you will have to change the time given,2hours and 15 minutes, into hours before you can use the formula mentioned above so that the total time is now written as 2 and 1 quarter hours or 2.25hrs.
We are now ready to begin.
1st Stage:
Using the formula, distance=speed*time we can replace the speed by the number 5 and the time by the letter T.
This gives us our first equation:
1st stage distance = 5*T=5T.(i)
2nd Stage:
In the same way we can get our second equation:
2nd stage distance = 8*t=8t.(ii)
We now need to find the total distance,that is,
5T+8t(iii).
Since the the distance of the 2nd stage is 2*distance of 1st stage then
8t=2*5T=10T(from (i) and (ii))
or 10T=8t.(iv)
Sharing both sides by 10 equation(iv)becomes:
T=0.8t
Now since the total time is 2.25hrs then
T+t=2.25.(v).
But T=0.8t so (v) becomes:
0.8t+t=2.25.
This simplifies to
1.8t=2.25(since t=1t).
Sharing both sides by 1.8 we get:
t=2.25/1.8=1.25hrs.
So T+1.25=2.25(from (v))
Hence T=2.25-1.25=1hr.
Finally then replacing T and t by their values in equation(iii) which represents the total distance we get:
5T+8t=5*1+8*1.25=5+10=15miles.
So the Walkathon was a distance of 15miles.
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