SOLUTION: q1) Together dien and jane eat 2/3 a pizza in 4 seconds. how long would it take each of them to eat the whole pizza alone if jane can eat a pizza 5 seconds faster than dien?
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Question 1177753: q1) Together dien and jane eat 2/3 a pizza in 4 seconds. how long would it take each of them to eat the whole pizza alone if jane can eat a pizza 5 seconds faster than dien?
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q2) Baba Yaga lost her broom somewhere between her hut and Bald Mountain, and wants to get it back. She calculates that with a tailwind of 2 km/ h, she can fly from her hut to Bald Mountain in 6 hours. Baba Yaga starts her trip, finds her broom 40 km before Bald Mountain, and turns around and flies home. The entire journey takes 9 hours. Find the speed Baba Yaga flies in quiet weather (with no tailwind or headwind).
Can someone explain step by step approach to solving this problem? Answer by ikleyn(52788) (Show Source):
Together they eat 2/3 pizza in 4 seconds -----------> hence, together they eat the entire pizza in 6 seconds.
Let x be the time for Dien in seconds to eat the pizza alone.
Then the time for Jane to eat the pizza alone is (x-5) seconds.
The rate of eating is for Dien and for Jane in terms of entire pizza per second.
The equation for the combined rate is
+ = .
To solve it, multiply both sides by 6x*(x-5). You will get then
6*(x-5) + 6x = x*(x-5)
Reduce to the standard quadratic equation
x^2 - 5x - 12x + 30 = 0
x^2 - 17x + 30 = 0
Factor left side
(x-15)*(x-2) = 0.
The only positive root x= 15 seconds for Dien provides the positive value (x-5) = 10 seconds for Jane.
ANSWER. 15 seconds for Dien and 15-5 = 10 seconds for Jane to eat the entire pizza alone.
