Answer:
A) 2.5
Explanation:
Extracting vital information from the question;
speed upstream = (v-3)mile/hr, distance traveled = 90 mile, speed downstream = (v+3), time for downstream in hours = t while time for upstream = t + 0.5 hr since the upstream journey is half hour longer.
speed = distance / time = 90 / (t + 0.5)
( v - 3) = 90 / ( t + 0.5)
cross multiply
(v-3) (t + 0.5) = 90 equation (1) for upstream motion
( v+3) = 90 / t
cross multiply
t(v+3) = 90 equation (2) for downstream motion
make v subject of the formula in equation 2
vt + 3t = 90
vt = 90 - 3t
divide both side by t
vt/t = (90 - 3t) / t
v = (90 - 3t) / t
substitute for t in equation 1
(( 90 - 3t) / t) - 3) (t + 0.5) = 90
solve through finding l.c.m ( lowest common multiple)
(90 - 3t - 3t)/ t (t + 0.5) = 90
(( 90 - 6t ) / t )(t + 0.5) = 90
open the brackets and cross multiply
90t + 45 - 6t² - 3t = 90 t
rearrange and collect the like terms
- 6t² - 3t + 45 = 90t - 90t
- 6t² - 3t + 45 = 0 multiply both side by -1
6t² + 3t - 45 = 0
divide both side by 3
2t² + t - 15 = 0
factorize the expression by multiplying - 15 by 2t² = - 30t²
find factors of - 30t² that adds to t = 6t × (-5t)
replace t with (+6t - 5t) in the equation
2t²+ 6t - 5t - 15 = 0
factorize
2t ( t + 3) - 5 ( t + 3) =0
(2t -5)(t + 3) = 0
2t - 5 = 0 or t + 3 = 0
2t = 5 or t = -3
divide through 2
2t / 2 = 5/ 2 = 2.5 or t = -3 since time cannot be negative
them t = 2..5 seconds
