Is 16.7 a reasonable sum for 7.5+9.2? Explain.

Mathematics

1 answer:

Xelga [282]4 years ago

4 0

Yes because 7.5 + 9.2= to 16.7 its your explation too

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Jeff bicycles 126 miles at the rate of r mph. The same trip would have taken 2 hours longer if he had decreased his speed by 4 m

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Given Information:

Distance = 160 miles

Required Information:

Rate = r = ?

Answer:

Rate = r = 20 mph

Step-by-step explanation:

Recall that the rate is given by

Rate = distance/time

$r = \frac{d}{t} \\\\t = \frac{d}{r} \\\\t = \frac{160}{r} \\\\$

It is given that the same trip would have taken 2 hours longer if he had decreased his speed by 4 mph.

Mathematically,

$\frac{160}{(r-4)} = \frac{160}{r} + 2 \\\\$

Simplify the equation

$\frac{160}{(r-4)} - \frac{160}{r} = 2 \\\\\frac{160r - 160(r-4)}{r(r-4)} = 2 \\\\\frac{160r - 160r+640)}{r(r-4)} = 2 \\\\160r - 160r+640 = r(r-4) (2) \\\\640 = r(r-4) (2) \\\\640 = (r^2 - 4r) (2) \\\\640 = 2r^2 - 8r \\\\2r^2 - 8r-640 =0 \\\\2(r^2 - 4r-320) =0 \\\\r^2 - 4r-320 =0 \\\\$