SOLUTION: At 10:30am two planes leave Houston, one flying east at 560 km/h and the other west at 640 km/h. At what time will they be 2100 km apart? I'm not sure what formula to put this i

Question 898281: At 10:30am two planes leave Houston, one flying east at 560 km/h and the other west at 640 km/h. At what time will they be 2100 km apart?
I'm not sure what formula to put this in to solve it. I believe the answer is 1 hr 45 min travel time so it would be 12:15pm. I know RxT=D, but how do I incorporate these in that formula. I'm confused.
I drew a picture and added the 2 rates together, so in 1 hr they are 1200 km apart. Then I added 30 min, so half of 1200 is 600 which would equal 1800 km. Then I added 15 min which would be half of 600 is 300. So 1200(1 hr) + 600(30 min) + 300(15 min) = 2100 km (1 hr 45 min). 10:30am + 1 hr 45min= 12:15pm
Found 2 solutions by mananth, MathTherapy:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
both are flying in opposite directions in a straight line
so the effective speed between them is 560 +640 km/h
= 1200 km/h
rate = 1200
d= 2100
time taken to be 2100 apart
2100/1200
= 1.75 hours
= 1hour 45 minutes
Answer by MathTherapy(10551) (Show Source): You can put this solution on YOUR website!
At 10:30am two planes leave Houston, one flying east at 560 km/h and the other west at 640 km/h. At what time will they be 2100 km apart?
I'm not sure what formula to put this in to solve it. I believe the answer is 1 hr 45 min travel time so it would be 12:15pm. I know RxT=D, but how do I incorporate these in that formula. I'm confused.
I drew a picture and added the 2 rates together, so in 1 hr they are 1200 km apart. Then I added 30 min, so half of 1200 is 600 which would equal 1800 km. Then I added 15 min which would be half of 600 is 300. So 1200(1 hr) + 600(30 min) + 300(15 min) = 2100 km (1 hr 45 min). 10:30am + 1 hr 45min= 12:15pm

At the time they are 2,100 km apart, both would have traveled distances that sum to 2,100 km
Let time it takes for them to be 2,100 km apart, be T
Thus, we have: 560T + 640T = 2,100
1,200T = 2,100
T, or time taken for both to be 2,100 km apart = , or hours, or 1 hour, 45 minutes after 10:30 am,
which is:
That makes you CORRECT, but you could've made the solution a lot easier.
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