Posted by Taylor on Monday, January 24, 2011 at 9:17pm.
Tom's speed = X m/s.
John's speed = (X + 5) m/s.
Tom's time = Ys.
John's time=(Y - 2.5)S.
Eq1: X*Y = 650m.
Y = 650/X.
Eq2:(X + 5)(Y - 2.5) = 650m.
In Eq2, substitute 650/X for Y:
(X + 5)(650/X - 2.5) = 650,
650 - 2.5X + 3250/X -12.5 = 650,
650 - 2.5X + 3250/X - 12.5 -650 = 0,
-2.5X + 3250/X -12.5 = 0,
Multiply each side by -X:
2.5X^2 - 3250 + 12.5X = 0,
Divide each side by 2.5:
X^2 + 5X - 1300 = 0,
Solve for X using Quad.Formula and get:
X = 33.64; X = -38.64.
Select positive value of X:
X = 33.64m/s = Tom's speed.
X*Y = 650,
33.64Y = 650,
Y = 19.3s = Tom's time.
X + 5 = 33.64 + 5 = 38.64m/s = John's
speed.
John's time = Y - 2.5 = 19.3 - 2.5 -
16.8S.
X - 20 = 0,
X + 25 =0,
X = -25.
Choose the positive solution:
X = 20m/s = Tom's speed.
X + 5 = 20 + 5 = 25m/s = John's speed.
XY = 650,
20Y = 650,
Y = 650 / 20 = 32.5s. = Tom's time.
Y -6.5 = 32.5 - 6.5=26s. = John's time.
;
OOPS!
Please disregard the 2nd (bottom)procedure.
Alternate Approach:
Tom's speed = X m/s.
Tom's time = Ys.
John's speed = (X + 5)m/s.
John's time = Y - 2.5 - 4 = Y - 6.5.
Eq1: XY = 650m. Y = 650/X.
Eq2: (X + 5)(Y - 6.5) = 6.5m.
Substitute 650/X for Y in Eq2:
(X + 5)(650/X - 6.5) = 650,
650 - 6.5X + 3250/X - 32.5 = 650,
650 - 6.5X + 3250/X -32.5 -650 = 0,
-6.5X + 3250/X -32.5 = 0,
Multiply each side by -X:
6.5X^2 - 3250 + 32.5X = 0,
Divide each term by 6.5:
X^2 + 5X - 500 = 0,
(X - 20)(X + 25) = 0,
X - 29 = 0,
X = 20.
X + 25 = 0,
X = -25.
Select positive value of X:
Tom's speed = X = 20m/s.
XY = 650,
20^Y = 650,
Tom's time = Y = 650/20 = 32.5s.
John's speed = X + 5 = 20 + 5 = 25m/s.
John's time = 32.5 - 2.5 = 30s.