Question

Two cars are traveling along perpendicular roads, car A at 40 mi/hr, car B at 60 mi/hr. At noon, when car A reaches the intersection, car B is 90 mi away, and moving toward it. At 1 p.m. the distance between the cars is changing, in miles per hour, at the rate of:

Answer 1

`(dD)/(dt) = -4 miles/hour`

negative sign indicates that the distance is decreasing with time

Step-by-step explanation:

Let at any time t after noon that is 12 p.m.

distance traveled by car A = 40t

distance traveled by car B = 90-60t

then distance between the two cars at time t

`D^2= (40t)^2+(90-60t)^2`............1

also, at time 1 p.m.

distance
`D^2= (40*1)^2+(90-60*1)^2`

D=50 Km

differentiating equation 1 w.r.t. t we get

`2D(dD)/(dt)= 2*40t*40+2(90-60t)(-60)`

put t= 1 and D= 50 we get

`2*50(dD)/(dt)= 3200*1-3600*1`

`(dD)/(dt) = -4 miles/hour`