Algebra

An air rescue plane averages
300 miles per hour in still air. It carries enough fuel for 5
hours of flying time. If, upon takeoff, it encounters a head
wind of 30 mi/hr, how far can it fly and return safely?
(Assume that the wind remains constant.)

A sugar molecule has twice
as many atoms of hydrogen as it does oxygen and one more
atom of carbon than oxygen. If a sugar molecule has a
total of 45 atoms, how many are oxygen? How many are
hydrogen?

The speed of a moving walkway is
typically about 2.5 feet per second. Walking on such a
moving walkway, it takes Karen a total of 40 seconds to
travel 50 feet with the movement of the walkway and then
back again against the movement of the walkway.What is
Karen’s normal walking speed?

A motorboat maintained a
constant speed of 15 miles per hour relative to the water in
going 10 miles upstream and then returning. The total time
for the trip was 1.5 hours. Use this information to find the
speed of the current.

Ans: 5 mi/hr.
Any solution for this? Thanks

A flash of lightning is seen, and
the resulting thunderclap is heard 3 seconds later. If the
speed of sound averages 1100 feet per second, how far away
is the storm?

Pedro can paint a fence 50% faster than Juan and 20% faster than Pilar and together they can paint a given fence in 4 hours. How long will it take Pedro to paint the same fence if he had to work alone?

Solution:
Let Rate of pedro = 1/tpedro = x
Rate of juan = .50x
Rate of pilar = .80x
(x+.50x+.80x)4=1
2.3x=1/4
x=5/46
5/46 = 1/tpedro
tpedro=46/5 =9.2hours

If a^x = b, b^y = c, and c^x = a, prove that the product xyz = 1.