Mathematics · May / June 2025 · Paper 42 · Question 24
0580
As printed in the paper
The question as text
Ahmed walks 2 km at a speed of x km/h. He then walks a further 3 km at a speed of ( ) x 1 É km/h. The total time he takes to walk the 5 km is 1 4 1 hours.
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24(a)[5]
2 3 5 + = oe + x x 1 4 2 × 4(x + 1) + 3 × 4x = 5x(x + 1) or ( ) 2 x + 1 3 x 5 + = ( ) ( ) + + x x 1 x x 1 4 8x + 8 + 12x = 5x2 + 5x oe Leading to 5x2 – 15x – 8 = 0 [6]
M2 M1 for 2 3 seen or seen x + x 1 M1 Correctly removing algebraic fractions or use of common denominator from their three-term equation with two fractions with different algebraic denominators M1 Correctly multiplying their brackets and clearing algebraic fractions from their three-term equation with two fractions with different algebraic denominators A1 With no errors or omissions
24(b)[3]
−− + − 2 − − [ ]15 ([ ]15) 4(5)( 8) oe 2(5) or 2 3 8 3 + + oe 2 5 2 3.46 [4]
B2 B1 for − −××−oe ([ ]15) 2 4 5 8 + − or for 15 p oe or 15 p oe 2(5) 2(5) 2 3 − or for x oe 2 B1
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