A life raft, set adrift from a sinking ship 150 miles offshore, travels directly toward a Coast Guard station at the rate of 5 miles per hour. At the time the raft is set adrift, a rescue helicopter is dispatched from the Coast Guard station. If the helicopter's average speed is 90 mph, how long will it take the helicopter to reach the life raft?

Let x = length of time it takes the helicopter to reach the life draft.

Raft Toward Coast Guard

Distance = 150 miles

rate = 5 mph

time = x

Coast Guard Toward Raft

Distance = 150 miles

rate = 90 mph

time = x

My equation is 5x + 90x = 150.

My answer for x is 1.59. The book's answer is 1 hour, 35 minutes.

What did I do wrong?