Andy is training for a long distance walk. He walks 7 km in the first week and then each week thereafter he increases his walk by 10%.How long will it take Andy to walk 20 km?

Question

BlackTom AI · Accepted Answer

We start by restating the problem in our own words to ensure understanding: Andy begins with a weekly distance of 7 km in the first week, and each subsequent week his distance increases by 10%. The question asks how long it will take to reach 20 km.

Option A:  A. 13 weeks. To evaluate this, we compute the distance for the nth week using the geometric progression: distance in week n is 7 × (1.1)^(n−1). We ask where this weekly distance becomes 20 or more. Solving 7 × (1.1)^(n−1) ≥ 20 gives (1.1)^(n−1) ≥ 20/7 ≈ 2.857. Taking natural logs, (n−1) × ln(1.1) ≥ ln(2.857) → (n−1) ≥ ln(2.857)/ln(1.1) ≈ 1.0498/0.0953 ≈ 11.0, so n ≥ 12. Thus, if we interpret “how long” to mean “in which week does the weekly distance first reach 20 km,” the answer would be around week 12. Week 13 (option A) is higher than the actual threshold and would imply waiting longer than necessary if we only require the weekly distance to reach 20. Therefore, this option overestimates the required week for the weekly distance to hit 20.

Option B:  B. 14 weeks. Similar reasoning as above shows that the weekly distance reaches 20 by about week 12, not as late as week 14. This option also overestimates the required week for achieving a 20 km weekly distance.

Option C:  C. 11 weeks. This is closer to the rough calculation (n ≈ 12) but still underestimates the week when the weekly distance first meets or exceeds 20. Since the computed threshold is just over 11 weeks, 11 would not yet reach 20 in the weekly distance model, making this option incorrect in this interpretation.

Option D:  D. 10 weeks. This is even farther from the threshold, and would definitely underestimate the week at which the weekly distance equals or surpasses 20. It is inconsistent with the logarithmic bound derived from 7 × (1.1)^(n−1) ≥ 20.

If instead the intended interpretation were the total cumulative distance over weeks, we would sum the weekly distances: S_k = 7 × (1.1^k − 1) / (1.1 − 1) = 70 × (1.1^k − 1). We would then solve 70 × (1.1^k − 1) ≥ 20, which yields 1.1^k ≥ 1.2857 and k ≥ log(1.2857)/log(1.1) ≈ 2.64, so k would be at least 3 weeks. In that interpretation, none of the given options (10–14 weeks) would be correct. The discrepancy suggests a possible misprint or mismatch between the question intent and the answer choices.

In summary, under the common interpretation that we seek the week in which the weekly distance first reaches or exceeds 20 km, the calculation yields n ≈ 12 weeks. Under the cumulative-sum interpretation, the result is about 3 weeks. Consequently, among the provided options, none precisely align with the standard calculations for these two interpretations, with 12 weeks being the closest match to the weekly-distance threshold and 3 weeks to the cumulative threshold.

Andy is training for a long distance walk. He walks 7 km in the first week and then each week thereafter he increases his walk by 10%.How long will it take Andy to walk 20 km?单项选择题

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