a boat can reach its destination in 3 hours. if it goes twice as fast it can reach 10 more miles more than its destination , in 2 hours. How ffast does it originally go?

Question

anonymous · Answer

Let's use a system of equations (all derived from distance= rate x time (d=rt))

 For the first scenario, time=3: d=3r > 3=d/r

 For the second scenario, rate = 2r (it's twice as fast), distance changes to d+10 (it went 10 miles further), and time = 2 (it took two hours): d+10=(2)(2r) > d=4r-10

 Substitute 4r-10 for d in the first equation to get: 3=(4r-10)/r. Solve for r and get 10.