Posted by Denis Borris on September 16, 2002 at 23:52:53:
In Reply to: word problems posted by Suzi on September 16, 2002 at 22:57:22:
: We need help with my son's math - On a recent 6 hour bike trip of 70 miles, Lila spent 2 hours on the first part of the trip where her average speed was half of her average speed on the second part. What was her speed on the first part? We have been given the answer which is 7 miles/hour. We must set up the problem. Any help???
To do these, always helpful to "draw" a sketch:
0H.....(m miles @ x mph)....2H...(70-m miles @ 2x mph)....6H.
Now you can SEE that during 1st 2 hours (0H to 2H),
a few miles (m) were travelled at the slower speed (x mph);
and you can SEE that during last 4 hours (2H to 6H),
the remaining miles (70-m) were travelled at twice
the 1st speed (2x mph).
Using the standard equation: speed = distance / time (/ means divided); you can set up 2 equations:
x = m / 2 [1]
2x = (70 - m) / 4 [2]
Now, substitute [1] in [2]:
2(m / 2) = (70 - m) / 4
Solve to get m = 14 (I'm assuming you can solve)
Now, substitute m = 14 in [1]:
x = 14 / 2
x = 7 (which is your answer)