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It takes a bicycle the same time to travel 7 miles as it takes a boat to travel 11 miles. If the boat is traveling 9mph faster than the bicycle, how fast is each traveling? Round answers to the nearest tenth place if necessary.

Solution

I t t ak es a bi cyc l e t h e s am e t im e t o t r a v e l 7 mi l es a s i t t ak es a b o a t t o t r a v e l 11 mi l es . I f t h e b o a t i s t r a v e l in g 9 m p h f a s t er t han t h e bi cyc l e, h o w f a s t i s e a c h t r a v e l in g ? R o u n d an s w ers t o t h e n e a res t t e n t h pl a ce i f n ecess a ry .

bicycl e^{'} s speed : 15.75

boa t^{'} s speed : 24.75

Solution steps

Translate the problem into an equation:

\frac{7}{x} = \frac{11}{x + 9}

Solve for

x, \frac{7}{x} = \frac{11}{x + 9} : x = \frac{63}{4}

Find speed

bicycl e^{'} s speed : 15.75

boa t^{'} s speed : 24.75