Suppose you get on a steamboat at noon in New Orleans and st

Suppose you get on a steamboat at noon in New Orleans and steam up the Mississippi River towards St. Louis at 20mph. Two hours later a friend gets in a motor boat in New Orleans and heads up river at 30 mph. What time does your friend catch up with you?

Solution

y=your time
a=a friends time
y=a+2
why a+2 because the friend is two hours later
20y=30a
rt=d
because they are going the same distance (catch up) we can set the two r*t\'s equal to each other.
substitute a+2 for y
20(a+2)=30a
20a+40=30a
40=10a
a=4
y=6
check
20y=30a
20(6)=30(4)
120=120
ok
noon+6=6pm
They went 120 miles up the Mississippi