Answer:
Step-by-step explanation:
Let's put in some numbers to make this easier to understand.
Let's say she has to travel 20 km.
On Monday, she travels at 4 kph. This takes 5 hours.
On Tuesday she travels 25% faster, at 5 kph. This takes 4 hours.
To figure percent reduction we take
100 % * (old - new) / old
100 % * (5 hr - 4 hr ) / 5 hr
100 % * 1 hr / 5 hr
100 % * 0.20
20% reduction.
Percentage reduction is how much a quantity has reduced, relative to another quantity.
Her percentage reduction in time is 20%
Let
[tex]v_1 \to[/tex] average speed on Monday
[tex]v_2 \to[/tex] average speed on Tuesday
From the question;
[tex]v_2 = v_1 \times (100\% + 25\%)[/tex] ---- 25% greater
[tex]v_2 = v_1 \times (125\%)[/tex]
[tex]v_2 = v_1 \times 1.25[/tex]
[tex]v_2 = 1.25v_1[/tex]
The percentage reduction from v2 to v1 is:
[tex]\% v = \frac{v_2 -v_1}{v_2}[/tex]
[tex]\% v = \frac{1.25v_1 -v_1}{1.25v_1}[/tex]
[tex]\% v = \frac{0.25v_1}{1.25v_1}[/tex]
[tex]\% v = \frac{0.25}{1.25}[/tex]
[tex]\% v = 0.2[/tex]
Represent as percentage
[tex]\% v = 0.2 \times 100\%[/tex]
[tex]\% v = 20\%[/tex]
Hence, the percentage reduction is 20%
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