Dennis = 12 km'h
Kathy = 20 km/h
Step-by-step explanation:
- Lets first establish that time is the same for both Kathy and Dennis and we can therefore assign is the value of <em>t</em>
- Kathy is cycling 8km/h faster than Dennis. Therefore if Dennis is doing <em>x </em>km/h Kathy is doing (<em>x</em>+8)km/h
- If it takes Kathy<em> t </em>time to cycle for 60 km at (<em>x</em>+8)km/h, we can derive the time <em>t </em>as;
(<em>x</em>+8)* <em>t </em>= 60
<em>t</em> = 60/(<em>x</em>+8)
- We can now use this time to establsish how fast Dennis is cycling. Dennis, using a speed of <em>x</em> km/h takes the same time (60/(<em>x</em>+8)) to cycle for 36 km. Therefore;
<em>x</em> * 60/(x+8) = 36
= 60x/(x+8) = 36
36 (x + 8) = 60x
36x + 288 = 60x
288 = 60x – 36x
288 = 24x
12 =<em> x </em>
Dennis is cycling at 12 km/h
Kathy is doing x + 8
= 12 + 8 = 20 km/h
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Represent your unknowns: Let s be the length of one side of the box. The relationship between s and x is s = x-4.
The volume of the box is (length)(width)(height), which here equals the following: V(x) = (x-4)*(x-4)*(x). You may either leave this result as is, or shorten it to V(x) = (x-4)^2*x, or expand (x-4)*(x-4)*(x).
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N=-13
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