SOLUTION: A person traveling 4 hr by plane and 25 hr by ship covers 1580 miles. If the speed of the plane had been one-half of the actual speed and the speed of the ship had been one-fourth

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 Question 145797: A person traveling 4 hr by plane and 25 hr by ship covers 1580 miles. If the speed of the plane had been one-half of the actual speed and the speed of the ship had been one-fourth greater, the person would have traveled only 1315 miles in the same length of time. Find the speeds of the plane and the ship.Answer by ankor@dixie-net.com(15638)   (Show Source): You can put this solution on YOUR website! person traveling 4 hr by plane and 25 hr by ship covers 1580 miles. If the speed of the plane had been one-half of the actual speed and the speed of the ship had been one-fourth greater, the person would have traveled only 1315 miles in the same length of time. Find the speeds of the plane and the ship. : Let x = speed of the plane and Let y = speed of the boat : "If the speed of the plane had been one-half of the actual speed, and the speed of the ship had been one-fourth greater, the person would have traveled only 1315 miles in the same length of time." Then .5x = speed of the plane and 1.25y = speed of the boat : When they say," the person would have traveled only 1315 miles in the same length of time." I assume they still mean 4 hrs in the plane and 25 hrs in the boat. If they mean only that the total time is 29 hrs it's a different problem. : Two equations: 4x + 25y = 1580 and .5(4x) + 1.25(25y) = 1315 2x + 31.25y = 1315 Multiply this equation by 2 and subtract the 1st equation from it 4x + 62.5y = 2630 4x + 25y = 1580 -------------------subtracting eliminates x 37.5y = 1050 y = y = 28 mph is the speed of the boat : Find the speed of the plane using the 1st equation: 4x + 25(28) = 1580 4x + 700 = 1580 4x = 1580 - 700 x = x = 220 mph is the speed of the plane : : Check using the "if" situation: 4(110) + 25(35) = 1315