SOLUTION: I just need help setting up the equation. It's from Algebra, Part 3 from Thomson Education Direct. It's a career oriented study unit. # of book is 2469C-1
A person travels 4 hrs
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A person travels 4 hrs
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Question 89511: I just need help setting up the equation. It's from Algebra, Part 3 from Thomson Education Direct. It's a career oriented study unit. # of book is 2469C-1
A person travels 4 hrs by plane and 25 hrs by ship and covers a total distance of 1580 miles. If the plane's speed would have been 1/2 of the actual speed and the ship's speed 1/4 greater than the actual speed, a distance of 1315 miles would have been travelled. Find the speeds of the plane and the ship. Found 2 solutions by scott8148, ankor@dixie-net.com:Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website! rate*time=distance ... p equals plane speed, s equals ship speed ... 4p+25s=1580 ... 4(p/2)+25(s(5/4))=1315
here are the equations ... let me know if you need help with the solution
You can put this solution on YOUR website! A person travels 4 hrs by plane and 25 hrs by ship and covers a total distance of 1580 miles. If the plane's speed would have been 1/2 of the actual speed and the ship's speed 1/4 greater than the actual speed, a distance of 1315 miles would have been traveled. Find the speeds of the plane and the ship.
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Let x = actual speed of the plane; and: y = actual speed of the ship
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Write 2 distance equations; Dist = time * speed:
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4x + 25y = 1580; actual speed equation
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We also have:
"If the plane's speed would have been 1/2 of the actual speed and the ship's speed 1/4 greater than the actual speed, a distance of 1315 miles "
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Equation for this would be: *4x + *25y = 1315
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Mult equation by 4 to get rid of these fractions and we have:
2(4x) + 5(25y) = 5260
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8x + 125y = 5260; the "if..." equation
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Multiply the actual equation by 2 and subtract it from the above equation
8x + 125y = 5260
8x + 50y = 3160
---------------- subtraction eliminates x
0x + 75y = 2100
y = 2100/75
y = 28 mph is the ships speed
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Use the actual speed equation to find x
4x + 25(28) = 1580
4x + 700 = 1580
4x = 1580 - 700
4x = 880
x = 880/4
x = 220 mph is the speed of the plane
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Check solutions in the "if.." equation *4(220) + *25(28) = 1315
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440 + 875 = 1315
;
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