Word Problem

Question

Two pirate ships 190 kilometers apart are headed straight toward each other—one at 50 kilometers per hour and the other at 80 kilometers per hour. A hero in a speedboat responds to the danger by racing back and forth between the ships, Unfortunately, when the hero reaches each ship, the pirates threaten him and he immediately turns the opposite direction and heads for the other ship. If the hero maintains a constant speed of 120 kilometers per hour the entire time—while speeding back and forth between the ships—how far will he have gone when the ships collide?

He will have gone how many kilometers? (Round to the nearest kilometer.)

Answer 1

distance=rate*time

the ships are headed toward each other and when they collide they will have covered 190 km together

190=50t+80t

190=130t

t=190/130

t=1.461538 hours

the two ships travel for 1.461538 hours before they collide

50*1.461538=73.0769 km traveled by the first ship

80*1.461538=116.9230 km traveled by the second ship

73.0769+116.9230=189.9999 km or approximately 190 km

the hero maintains a constant speed of 120 km per hour for 1.461538 hours (this is when the ships collide)

d=rt

d=(120)(1.461538)

d=175.3845 km

d=175 km is how far the hero travels before the ships collide

Answer 2

Hi Jesse,

 

Use the equation Speed = Distance/time

The ships are travelling at a relative velocity of (50+80) = 130 km/hr

They will collide after t = 190/130 hr = 1.46 hrs

In 1.46 hrs hero would have traveled 120*1.46 = 175 km.