Question 616060: At the beginning of a walk Rob and Juan are 4.4 miles apart. If they leave at the same time and walk in the same direction, Rob will overtake Juan in 11 hours. If they walk towards each other they meet in 1 hour. What are their speeds?
Answer by dragonwalker(73)   (Show Source):
You can put this solution on YOUR website! Okay, so if they walk toward each other and it takes 1 hour then their cumulative speed must be 4.4 miles per hour (mph). Let us say that Rob's speed is r and Juan's speed is j.
So r + j = 4.4 mph
Now as Rob catches up with Juan he must start from behind and is walking faster than Juan, but how much faster?
Well, over 11 hours he walks an extra 4.4 miles.
So his speed compared to Juan's is 4.4 miles divided by 11 hours faster
= 4.4/11
= 0.4 mph faster than Juan
so as Juan's speed is j then Rob's speed is j + 0.4
Now we said that Rob's speed is r. If we write it using the above formula:
r = j + 0.4
Now if look at the first equation r + j = 4.4
We can replace the r with (j + 0.4) as so:
(j + 0.4) + j = 4.4
j + 0.4 + j = 4.4
and solve for j: ( we move the 0.4 to the right side. When we change the side of a number we have to change it's sign (in this case from positive to negative). We also add the j's together. :
2j = 4.4 - 0.4
2j = 4.0
j = 2.0
So Juan walks at 2 mph
We know that Rob walks 0.4 mph faster than Juan so Rob walks at
2.0 + 0.4 = 2.4 mph !!!
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