SOLUTION: Ranjit is journeying by foot and on horseback to a remote place. She can travel 3 miles in an hour on foot or 7 miles in an hour on horseback. After 10 hours, she has traveled 46 m

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Question 939761: Ranjit is journeying by foot and on horseback to a remote place. She can travel 3 miles in an hour on foot or 7 miles in an hour on horseback. After 10 hours, she has traveled 46 miles. How many hours has she traveled on foot and on horse?
A. 6 hours on foot and 4 hours on horse
B. 5 hours on foot and 5 hours on horse
C. 7 hours on foot and 3 hours on horse
D. 8 hours on foot and 2 hours on horse

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose she traveled x hours on foot.
Total time t=+10 hours so she traveled %2810-x%29 hours on horseback.
Therefore, on foot she traveled 3%2Ax miles
and on horseback she went 7%2A%2810-x%29=70-7x miles.
In total, that is 3x+%2B+70+-+7x+=+70+-+4x
The total distance traveled was 46 miles so that 70+-+4x+=+46
Therefore 4x+=+70-46+=+24 and so x+=+24%2F4+=+6 hours.
x+=+6 hours on foot and 10-x=10-6=4 hours on horseback
so, answer is A.6 hours on foot and 4 hours on horse