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2

Part of 2022 AMC 10

Problems(2)

Mike the Cyclist

Source: 2022 AMC 10A #2

11/11/2022
Mike cycled 1515 laps in 5757 minutes. Assume he cycled at a constant speed throughout. Approximately how many laps did he complete in the first 2727 minutes?
<spanclass=′latex−bold′>(A)</span>5<spanclass=′latex−bold′>(B)</span>7<spanclass=′latex−bold′>(C)</span>9<spanclass=′latex−bold′>(D)</span>11<spanclass=′latex−bold′>(E)</span>13<span class='latex-bold'>(A) </span> 5 \qquad <span class='latex-bold'>(B) </span> 7 \qquad <span class='latex-bold'>(C) </span> 9 \qquad <span class='latex-bold'>(D) </span> 11 \qquad <span class='latex-bold'>(E) </span> 13
AMC 10AMC2022 AMC2022 AMC 10aratesrate problems
Simple Rhombus

Source: 2022 AMC 10B #2 / 2022 AMC 12B #2

11/17/2022
In rhombus ABCDABCD, point PP lies on segment AD‾\overline{AD} such that BP⊥ADBP\perp AD, AP=3AP = 3, and PD=2PD = 2. What is the area of ABCDABCD?
[asy] import olympiad; size(180); real r = 3, s = 5, t = sqrt(r*r+s*s); defaultpen(linewidth(0.6) + fontsize(10)); pair A = (0,0), B = (r,s), C = (r+t,s), D = (t,0), P = (r,0); draw(A--B--C--D--A^^B--P^^rightanglemark(B,P,D)); label("AA",A,SW); label("BB", B, NW); label("CC",C,NE); label("DD",D,SE); label("PP",P,S); [/asy] <spanclass=′latex−bold′>(A)</span>35<spanclass=′latex−bold′>(B)</span>10<spanclass=′latex−bold′>(C)</span>65<spanclass=′latex−bold′>(D)</span>20<spanclass=′latex−bold′>(E)</span>25<span class='latex-bold'>(A) </span>3\sqrt 5 \qquad <span class='latex-bold'>(B) </span>10 \qquad <span class='latex-bold'>(C) </span>6\sqrt 5 \qquad <span class='latex-bold'>(D) </span>20\qquad <span class='latex-bold'>(E) </span>25
geometryAMCAMC 122022 AMCAMC 102022 AMC 10B2022 AMC 12B