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Brianna left the bookstore traveling 32 mph. Then 3.2 hours later, Sonya left traveling the same direction at 44.8 mph. How long until Sonya catches up with Brianna

Respuesta :

frika

Answer:

8 hours

Step-by-step explanation:

Let t hours be the time needed Sonya to catch up Brianna.

Sonya:

Time = t hours

Rate = 44.8 mph

Distance [tex]=D_S[/tex] miles

Brianna

Time [tex]=t+3.2[/tex] hours

Rate = 32 mph

Distance [tex]=D_B[/tex] miles

Note that [tex]D_S=D_B,[/tex] because Sonya must catch up Brianna.

Use formula [tex]D=r\cdot t[/tex]

Hence,

[tex]44.8t=32(t+3.2)[/tex]

Solve this equation:

[tex]44.8t=32t+32\cdot 3.2\\ \\44.8t-32t=102.4\\ \\12.8t=102.4\\ \\t=8[/tex]

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