The distance is 145 miles. A truck can cover this distance in 2.5 hours. A car is 1.5 times as fast as the truck. How long does it take them to meet, if they start moving towards each other same time?

Answer 1

Hi Larry,

Step 1: Find the speed of both trucks.

Distance=(Rate)(Time)

Rearranging this equation, we get Rate= (distance)/(time)

The truck's speed is: Rate=(145mi)/(2.5hr)=58mph

The car's speed is "1.5 times as fast as the car": (truck)(1.5)=(58)(1.5)=87mph

Step 2: Figure out how long it takes the car and truck to meet. In other words, at what time does the distance traveled by the truck equal the distance of the car.

Car's Distance+ Truck's Distance= total distance

(car rate)(time) + (truck rate)(time)=145

(58)(time) + (87)(time)=145 Substitute

145(time)=145 Divide both sides

time= 145/145

time=1

∴It takes the car and truck one hour to meet.

Best,

Starlyte

Answer 2

The truck's speed is 145/2.5 or 58 mph. The car is 1.5 faster or moving at 87 mph. Assuming the car doesn't get pulled over for speeding, both will have traveled for the same amount of time, so

58T+87T=145 -> 145T=145 -> T=1

They will meet in exactly 1 hour.