SOLUTION: vehicle a and vehicle b are 10 mi apart.vehicle a travels 20 mph. vehicle b travels 30 mph. veh a travels perpindicular to a line between veh a and veh b. both vehs start at same t

Question 700936: vehicle a and vehicle b are 10 mi apart.vehicle a travels 20 mph. vehicle b travels 30 mph. veh a travels perpindicular to a line between veh a and veh b. both vehs start at same time. veh b must intercept veh a in shortest distance. what is the distance?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
vehicle a and vehicle b are 10 mi apart.vehicle a travels 20 mph.
vehicle b travels 30 mph.
veh a travels perpendicular to a line between veh a and veh b.
both vehs start at same time. veh b must intercept veh a in shortest distance.
what is the distance?
:
The perpendicular paths to intercept form a right triangle, with a hypotenuse of 10 mi
:
Find the travel time, then we can find the distance that b travels to intercept
Let t = travel time
:
Using pythag: a^2 + b^2 = c^2
(20t)^2 + (30t)^2 = 10^2
400t^2 + 900t^2 = 100
simplify, divide by 100
4t^2 + 9t^2 = 1
13t^2 = 1
t =
t = .27735 hrs to intercept
distance traveled by veh b
.27735(30) = 8.32 mi
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