Word Problems
Two plane leave Sligo Ireland flying at the same time, at right angles, one going east the other south. If one plane is
flying at a speed of 90 km slower than the other plane and after 2 hours they are 540 km apart
what is the speed of each plane?
- x = the speed of the slower plane;
- x + 90 = the speed of the faster plane
- To solve the problem you need the Pythagorean theorem c2 = a2 + b2
- c will equal the 540 km; a = 2x (why is it 2x and not just x? Try to answer the question before checking the answer. answer );
b = 2(x + 90)
- 5402 = (2x)2 + (2(x+90))2
- 5402 = (2x)2 + (2x+180))2
- 291600 = 4x2 + 4x2 + 720x + 32,400
- 291600 = 8x2 + 720x + 32,400
- 0 = 8x2 + 720x - 259200
- 0 = x2 + 90x - 32400
- 0 = x2 + 90x - 32400
- Use the quadratic formula to solve the equation.
- x = 140.54 km per hour (slower plane); 2nd plane - 230kmph
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