Work Problem 1 Solution

In this Algebra work word problem solution the way to figure out the answer is to realize that they work a fractional part of work each hour. So in 1 hours time Steve does 1/9 of his work, so in 9 hours he does 9/9 or his whole job. Same thing goes for Joe except he gets 1/10th of his job done in an hour. For just one guy, take Steve for instance, the algebra for his work by himself would be (1/9)x = 1 or x/9 = 1 which makes x = 9 or 9 hours. for Joe it would be x/10 = 1 or 10 hours. Together they would take x/9 + x/10 = 1 hours(x) to get the job done.

x/9 + x/10 = 1
multiply by 90
10x + 9x + 90
19x = 90
x = 90/19

90/19 = 4.74 or approximately 4 hours and 45 minutes (.75 would 3/4ths of an hour or 45 minutes). If you want it exact just take the fractional part(.7368) and multiply by 60. You'll end up with 44.2 which is 44 minutes and .2*60 seconds or 12 seconds. The detailed answer would be 4 hours 44 minutes and 12 seconds. So if he hires both of these guys he'll get the lawn mowed before 6 hours.

Time Distance Problem 6 Solution

In this Algebra word problem solution, an non-algebraic approach would be looking at far Bob goes in 1 hour, since he has an hour head start. He's going 60 mi/hr so he went 60 miles in 1 hour. Steve is going 90 mi/hr or 30 mi/hr faster. So how long would it take someone going 30 mi/hr to go 60 miles? Well the 1st hour he went 30 miles, the 2nd hour he goes the other 30 or 2 hours total until he catches up to Bob. If your going 90 miles an hour for 2 hours-- you have gone 90 * 2 or 180 miles.

Algebraic approach:

x = time

rate * time = distance

60 = # of miles per hour Bob is going

90 = # of miles per hour Steve is going

x + 1 = the hour head start Bob had

Bob = 60(x+1)

Steve = 90x

Since Bob & Steve are going the same distance we can set their respective distance * time equal to one another.

60(x+1) = 90x
60x + 60 = 90x
60 = 30x
30x = 60
x =60/30
x = 2 or 2 hours

check
60(2+1) = 90(2)
180 = 180 --- rate times time = distance which is the answer to the 2nd part of the problem they went 180 miles total.....