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viva [34]
3 years ago
15

When the Slowpoke Marathon began, the ratio of runners to joggers was 2 to 19. A total of 4200 participants began the race (each

either a runner or a jogger, but not both), but 450 joggers dropped out of the race along the way. Out of the remaining participants, who are runners, 16 % of them dropped out of the race. If everyone else finished the race, then what was the simplified ratio of runners to joggers among those who finished the race?
Mathematics
2 answers:
NeTakaya3 years ago
8 0

Answer:

  168 : 1675

Step-by-step explanation:

At the beginning of the race, the number of ratio units was 2+19 = 21, so each stands for 4200/21 = 200 participants. Then there were ...

  • 2×200 = 400 runners
  • 19×200 = 3800 joggers

At the end of the race, there were 450 fewer joggers, so ...

  3800 -450 = 3350 . . . joggers

16% of the 400 runners is 64 runners, so with that many dropping out, the remaining number of runners was ...

  400 -64 = 336

So, at the end of the race the ratio of runners to joggers was ...

  336 : 3350 = 168 : 1675

marin [14]3 years ago
7 0

Answer:

168 : 1675

Step-by-step explanation:

2/21 × 4200 = 400 runners

19/21 × 4200 = 3800 joggers

3800 - 450 = 3350 joggers

400 - 16%(400) = 336 runners

336 : 3350

168 : 1675

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Two airplanes are flying in the air at the same height. Airplane A is flying east at 300mi/h and airplane B is flying north at 2
Ipatiy [6.2K]

Answer:

\frac{dAB}{dt}=340 mil/h

Step-by-step explanation:

The change of distance over time of the plain A is 300 mi/hour and 200 mi/hour for plane B. O is the point of the airport.

So, the distance from A to O AO = 90 miles and BO = 120 miles.

Now, we have a right triangle here.  We can use the Pythagorean theorem, so the distance between the planes will be:

AB^{2} =AO^{2}+BO^{2} (1)

AB =\sqrt{AO^{2}+BO^{2}}=

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If we take the derivative of the equation (1) we could find the change of the distance between planes.

2AB\frac{dAB}{dt}=2AO\frac{dAO}{dt}+2BO\frac{dBO}{dt}

2*150\frac{dAB}{dt}=2*90*300+2*120*200=102000 mil/h

\frac{dAB}{dt}=\frac{102000}{150*2}

Finally,

\frac{dAB}{dt}=340 mil/h

I hope it helps you!

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