A boat can go 72 miles downstream in 3 hours, and can make the return trip in 4 hours. Find the speed of the boat in still water.

up: (s+c)3=72, 
down: (s-c)4=72 

adding... 
2s=72(1/3+1/4) 

then... 
s=21 
boat speed: 21mph

Alan participated in a car race in which he had to cover a distance of at least 50 kilometers. He had fuel in his car for a maximum distance of 53 kilometers. If the distance is given by S(t)=3t+47 , where (t) is the time in hours, find the minimum and maximum number of hours for which Alan can drive his car.

so


In general his limits are:

but assuming he wants to stay in the race:


and his limits are:

find the two positive integers required if the sum of a positive integer and its square is 30? find the number

so the number is 5

Two trains are on the same track going in opposite directions. One is traveling at 55 mph and the other is traveling at 45 mph and they are 250 miles apart. How long until they hit?

Speed:
s=d/t 
Trains moving toward each other means their speeds add - so we write: 
t=d/s=250/(55+45)=2.5 

2 and 1/2 hours 

:)

If a car traveled for 3 hours at r mph and increased the speed by 10 mph and traveled for 1 more hour hour, how far did the car travel?

3 hours at r mph:
 
increased the speed by 10 mph and traveled for 1 more hour hour: 
 

total: