Mathematics · Oct / Nov 2025 · Paper 41 · Question 24
0580
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The question as text
Martha walks a distance of 10 km at a speed of x km/h. She then runs a distance of 5 km at a speed of ( ) x 4 Ì km/h. The total time taken for the whole journey is 3.5 hours.
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24(a)[1]
10 x [1]
24(b)[4]
their10 5 7 + = oe + x x 4 2 20 x + 80 + 10 x = 7 x 2 + 28 x oe − − = Leading to 7 x 2 2 x 80 0 [5]
M1 M2 Strict FT for correctly clearing fractions from their three-term equation with two algebraic denominators in x and x + 4 and expanding all brackets Strict M1FT for correctly expressing their two algebraic fractions with two denominators in x and x + 4 as a single fraction or with a common denominator within a correct equation or for correctly clearing fractions from their three-term equation with two algebraic denominators in x and x + 4 but not all brackets expanded A1 No errors or omissions
24(c)[3]
( ) ( )( ) −− ± − 2 − − 2 ([ ]2) 4 7 80 oe ( ) 2 7 –3.24 and 3.53 [4]
B2 or B1 for − − ( )( − ) ([ ]2) 2 4 7 80 oe or for −− − −− + ( 2) p oe or for ( 2) p oe 2(7) 2(7) 2 2 − or x 14 B1
24(d)[3]
2h 10min [3]
B2 for 2.168 to 2.18 [h] or for 130.08 to 130.8 [min] or for 2hours 10.08 min to 2 hours 10.8 min OR 10 5
M2 for − + their positive x their positive x 4 or 10 5
M1 for or their positive x + their positive x 4
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