<p>Every morning Aya goes for a <img alt="$9$" height="12" src="https://latex.artofproblemsolving.com/b/f/2/bf2c9074b396e3af0dea52d792660eea1c77f10f.png" width="8" />-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of <img alt="$s$" height="8" src="https://latex.artofproblemsolving.com/f/3/7/f37bba504894945c07a32f5496d74299a37aa51c.png" width="8" /> kilometers per hour, the walk takes her 4 hours, including <img alt="$t$" height="11" src="https://latex.artofproblemsolving.com/e/0/d/e0d2bf360290fd61d1c1557e763f2622363b3d35.png" width="6" /> minutes spent in the coffee shop. When she walks <img alt="$s+2$" height="15" src="https://latex.artofproblemsolving.com/1/e/2/1e2befa15a2ef30c53994455e1f3dcd36fbc30a7.png" width="42" /> kilometers per hour, the walk takes her 2 hours and 24 minutes, including <img alt="$t$" height="11" src="https://latex.artofproblemsolving.com/e/0/d/e0d2bf360290fd61d1c1557e763f2622363b3d35.png" width="6" /> minutes spent in the coffee shop. Suppose Aya walks at <img alt="$s+\frac{1}{2}$" height="38" src="https://latex.artofproblemsolving.com/2/4/d/24dea3f5792637bdb03e958be9a46b2c092a4879.png" width="46" /> kilometers per hour. Find the number of minutes the walk takes her, including the <img alt="$t$" height="11" src="https://latex.artofproblemsolving.com/e/0/d/e0d2bf360290fd61d1c1557e763f2622363b3d35.png" width="6" /> minutes spent in the coffee shop.</p>

Question No: 310

Every morning Aya goes for a $9$ -kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, including $t$ minutes spent in the coffee shop. Suppose Aya walks at $s+\frac{1}{2}$ kilometers per hour. Find the number of minutes the walk takes her, including the $t$ minutes spent in the coffee shop.

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Tags: Algebra Combinatorics Geometry Probability

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