Maria bicycles 8 ​km/h faster than Carlos. In the same time it takes Carlos to bicycle 54 km comma Maria can bicycle 78 km. How fast does each bicyclist​ travel?

1 Answer
Somebody N.
May 7, 2018

#color(blue)("Carlos' speed"=18kmh^(-1))#

#color(blue)("Maria's' speed"=26kmh^(-1))#

Explanation:

Let:

#s="Carlos' speed"#

Maria's speed is #8kmh^(-1)# faster, so Maria's speed is:

#(s+8)kmh^(-1)#

Using:

#"time"="distance"/"speed"#

Carlos' time to cycle #54km# is:

#"time"=54/s#

Maria's time to cycle #78km# is:

#"time"=78/(s+8)#

They both complete these distances in the same time, so we can say:

#54/s=78/(s+8)#

We solve this for #s#:

#54(s+8)=78s#

#54s+432=78s#

#24s=432#

#s=432/24=18#

#s="Carlos' speed"#, so:

Carlos' speed is #18kmh^(-1)#

Maria's speed was #8kmh^(-1)# faster, so:

#s+8=>18+8=26#

Maria's speed was:

#26kmh^(-1)#

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