Question 89511
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.
:
Let x = actual speed of the plane; and: y = actual speed of the ship
:
Write 2 distance equations; Dist = time * speed:
:
4x + 25y = 1580; actual speed equation
:
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 "
:
Equation for this would be:
{{{1/2)}}}*4x + {{{5/4}}}*25y = 1315
:
Mult equation by 4 to get rid of these fractions and we have:
2(4x) + 5(25y) = 5260
:
8x + 125y = 5260; the "if..." equation
:
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
:
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
:
Check solutions in the "if.." equation
{{{1/2)}}}*4(220) + {{{5/4}}}*25(28) = 1315
:
440 + 875 = 1315
;
:
Did this help you?