SOLUTION: Cross-country cycling. Erin was traveling across the desert on her bicycle. Before lunch she traveled 60 miles (mi); after lunch she traveled 46 mi. She put in 1 hour more after

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Question 191981This question is from textbook
: Cross-country cycling. Erin was traveling across the
desert on her bicycle. Before lunch she traveled 60 miles
(mi); after lunch she traveled 46 mi. She put in 1 hour
more after lunch than before lunch, but her speed was
4 mph slower than before. What was her speed before
lunch and after lunch?
I tried solving this problem by using the d=r(t) equation.
x=rate y=time
before lunch= 60/x=y
after lunch= 48/x-4=y+1
so I substituted 60/x for y
46/x-4=60/x +1
46x=60(x-4) +x(x-4)
46x= 60x-240+x^2-4x
46x=x^2+56x-240
0=x^2+10x-240
I plug this into the quadratic formula, and it doesn't work, any suggestions?
This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You're on the right track, you just need to solve the equation 0=x%5E2%2B10x-240


0=x%5E2%2B10x-240 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=10, and c=-240


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%2810%29+%2B-+sqrt%28+%2810%29%5E2-4%281%29%28-240%29+%29%29%2F%282%281%29%29 Plug in a=1, b=10, and c=-240


x+=+%28-10+%2B-+sqrt%28+100-4%281%29%28-240%29+%29%29%2F%282%281%29%29 Square 10 to get 100.


x+=+%28-10+%2B-+sqrt%28+100--960+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-240%29 to get -960


x+=+%28-10+%2B-+sqrt%28+100%2B960+%29%29%2F%282%281%29%29 Rewrite sqrt%28100--960%29 as sqrt%28100%2B960%29


x+=+%28-10+%2B-+sqrt%28+1060+%29%29%2F%282%281%29%29 Add 100 to 960 to get 1060


x+=+%28-10+%2B-+sqrt%28+1060+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-10+%2B-+2%2Asqrt%28265%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-10%29%2F%282%29+%2B-+%282%2Asqrt%28265%29%29%2F%282%29 Break up the fraction.


x+=+-5+%2B-+1%2Asqrt%28265%29 Reduce.


x+=+-5%2Bsqrt%28265%29 or x+=+-5-sqrt%28265%29 Break up the expression.


So the answers are x+=+-5%2Bsqrt%28265%29 or x+=+-5-sqrt%28265%29


which approximate to x=11.279 or x=-21.279



However since "x" is a speed and a negative speed doesn't make sense, this means that the only answer is x+=+11.279


So her speed before lunch was approximately 11.279 mph and her speed after lunch was about 7.279 mph