Jen recently rode her bicycle to visit her friend who lives 6 miles away. On her way there, her average speed was & miles per hour faster than on her way home. If jen spent a total of 2 hours bicycling find the two rates.

Let +s+ = her average speed going back home

+s+%2B+5+ = her average speed going to friend's house

Let +t+ = her time in hrs going back home

+2+-+t+ = her time in hrs going to friend's house

Equation for going to friend's house:

(1) +12+=+%28+s+%2B+5+%29%2A%28+2+-+t+%29+

Equation for going back home:

(2) +12+=+s%2At+

(2) +t+=+12%2Fs+

Plug this result back into (1)

(1) +12+=+%28+s+%2B+5+%29%2A%28+2+-+12%2Fs+%29+

(1) +12+=+2s+%2B+10+-+12+-+60%2Fs+

(1) +14+=+2s+-+60%2Fs+

(1) +14s+=+2s%5E2+-+60+

(1) +2s%5E2+-+14s+-+60+=+0+

(1) +s%5E2+-+7s+-+30+=+0+

(1) +%28+s+-+10+%29%2A%28+s+%2B+3+%29+=+0+ ( by looking at it )

(1) +s+=+10+ ( can't use the negative solution )

and

+s+%2B+5+=+15+

Going to friend's house: 15 mi/hr

Going back home: 10 mi/hr

check:

(2) +12+=+s%2At+

(2) +12+=+10t+

(2) +t+=+1.2+ hrs

and

(1) +12+=+%28+s+%2B+5+%29%2A%28+2+-+t+%29+

(1) +12+=+15%2A%28+2+-+t+%29+

(1) +12+=+30+-+15t+

(1) +15t+=+30+-+12+

(1) +15t+=+18+

(1) +t+=+1.2+ hrs

Step-by-step explanation:

hope it help brainliest pls

(1) +t+=+1.2+ hrs

Step-by-step explanation:

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