Joe is driving west at 60km/h and Dave is driving south at 70 km/h. Both cars are approaching the intersection of the two roads. At what rate is the distance between the cars decreasing when Joe's car is 0.4 km and Dave's is 0.3 km from the intersection

So rate of increase of distance along line of joining = 42 + 48 = 90 km/h

Step-by-step explanation:

Joe is driving west at 60 km/h and Dave is driving south at 70 km/h. Both cars are approaching the intersection of the two roads.

We have to find the rate at which the distance between the cars is decreasing when Joe's car is 0.4 km and Dave's is 0.3 km from the intersection.

The rate at which the distance is decreasing the sum of the speeds of the 2 cars along the line joining the 2 cars at that instant.

Component of speed of Joe = 60 cos (37°) = 48 km/h

Component of speed of Dave = 70 cos (53°) = 42 km/h

So rate of increase of distance along line of joining = 42 + 48 = 90 km/h