Thread: Help with some algebra 2 word problems.

1. A commercial jet can fly from San Francisco to Dallas in 3 hours. A private jet can make the same trip in 3.5 hours. If the two planes leave San Francisco at noon, after how many hours is the private jet twice as far from Dallas as the commercial jet? The answer is 21/8 hours or 2 and 5/8 hours, just need to know how to get there. >.<

2.A car radiator is filled with 5 liters of a 25% antifreeze solution. How many liters must be drawn off and replaced by a 75% antifreeze solution to leave the car radiator fillers with a 55%antifreeze solution? Don't have the answer to this one.

3.The rail line between two cities consist of two segments, one 96 km longer than the other. A passenger train averages 60 km/h over the shorter segment, 120 km/h over the longer, and 100 km/h for the entire trip. How far apart are the cities? The answer is 160 km, just need to see how to get there.

thanks in advance : D

Hi, and welcome to the forum.

Please see rules #8 and #11 (and the rest) in this thread.

1. A commercial jet can fly from San Francisco to Dallas in 3 hours. A private jet can make the same trip in 3.5 hours. If the two planes leave San Francisco at noon, after how many hours is the private jet twice as far from Dallas as the commercial jet?

Let d be the distance between San Francisco and Dallas. Express the speed of each jet through d. Further, let t be the required time. Find the distance traveled by each jet in time t, and then find the remaining distance for each jet. Finally, form an equation saying that the remaining distance for the private jet is twice the remaining distance for the commercial jet. The distance d should cancel at this point.

2.A car radiator is filled with 5 liters of a 25% antifreeze solution. How many liters must be drawn off and replaced by a 75% antifreeze solution to leave the car radiator fillers with a 55%antifreeze solution?

Let x be the number of liters of the solution that have to be drawn off. Let a1 be the total initial volume of antifreeze, a2 be the volume of 25% antifreeze in x (this much is drawn off) and a3 be the volume of 75% antifreeze in x (this much is added, since the final solution volume is again 5 liters). Then the total final volume of antifreeze is a1 - a2 + a3 and the concentration is (a1 - a2 + a3) / 5 = 0.55. Express a1, a2 and a3 through x and form an equation on x.

3.The rail line between two cities consist of two segments, one 96 km longer than the other. A passenger train averages 60 km/h over the shorter segment, 120 km/h over the longer, and 100 km/h for the entire trip.

Let d be the length of the shorter segment; express the longer segment and the total distance through d. Since the average speeds over each of the segment and the total trip are given, find the time for each segment and for the whole trip. Adding the first two numbers gives the third one.